Trigonometry Formulas for SSC CGL PDF: Basic and Advanced

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is an important part of the SSC CGL exam and candidates who want to do well on the exam need to have a strong understanding of trigonometry.

This article provides a PDF of the most important trigonometry formulas for the SSC CGL exam. The PDF includes formulas for basic trigonometric functions, such as sine, cosine, and tangent. It also includes formulas for more advanced trigonometric functions, such as trigonometric identities and trigonometric equations.

In addition to the PDF, this article also provides an introduction to trigonometry and a discussion of why trigonometry is important for the SSC CGL exam. The article also provides some tips on how to prepare for trigonometry questions on the SSC CGL exam.

We hope that this article and the PDF will help you to prepare for the trigonometry section of the SSC CGL exam. Good luck!

Here are some of the reasons why trigonometry is important for the SSC CGL exam:

• Trigonometry is a fundamental part of mathematics, and it is used in many different areas of the exam.
• Trigonometry questions are often used to test problem-solving skills, which are essential for success on the SSC CGL exam.
• Trigonometry questions can be challenging, but they can also be very rewarding to answer correctly.

By learning the trigonometry formulas in the PDF and practicing solving trigonometry problems, you can improve your chances of success on the trigonometry section of the SSC CGL exam.

Basic trigonometric functions

The basic trigonometric functions are used to solve problems involving triangles, and they are also used in many other areas of mathematics, such as calculus and physics.

• Sine (sin): The sine of an angle is the ratio of the opposite side to the hypotenuse of a right triangle.
• Cosine (cos): The cosine of an angle is the ratio of the adjacent side to the hypotenuse of a right triangle.
• Tangent (tan): The tangent of an angle is the ratio of the opposite side to the adjacent side of a right triangle.
• Cotangent (cot): The cotangent of an angle is the reciprocal of the tangent of an angle.
• Secant (sec): The secant of an angle is the reciprocal of the cosine of an angle.
• Cosecant (csc): The cosecant of an angle is the reciprocal of the sine of an angle.

Here are some examples of how the basic trigonometric functions can be used to solve problems involving triangles:

• To find the missing side of a right triangle, you can use the sine, cosine, or tangent function to relate the missing side to the other two sides.
• To find the area of a triangle, you can use the sine function to relate the area to the base and the height of the triangle.
• To find the volume of a pyramid, you can use the sine function to relate the volume to the area of the base and the height of the pyramid.

Trigonometric identities

These identities are very useful for simplifying trigonometric expressions and solving trigonometric equations.

• Pythagorean identity: This identity states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

a² + b² = c²

• Sine addition formula: This formula gives the sine of the sum of two angles.

sin(α + β) = sin α cos β + cos α sin β

• Cosine addition formula: This formula gives the cosine of the sum of two angles.

cos(α + β) = cos α cos β - sin α sin β

• Tangent addition formula: This formula gives the tangent of the sum of two angles.

tan(α + β) = (tan α + tan β) / (1 - tan α tan β)

• Sine subtraction formula: This formula gives the sine of the difference of two angles.

sin(α - β) = sin α cos β - cos α sin β

• Cosine subtraction formula: This formula gives the cosine of the difference of two angles.

cos(α - β) = cos α cos β + sin α sin β

• Tangent subtraction formula: This formula gives the tangent of the difference of two angles.

tan(α - β) = (tan α - tan β) / (1 + tan α tan β)

Trigonometric equations are equations that involve trigonometric functions. Some examples of trigonometric equations include:

• sin x = 1/2
• cos 2x = √3/2
• tan x = √3

Trigonometric equations 

Solving trigonometric equations is the process of finding all the solutions to a trigonometric equation. There are many different methods for solving trigonometric equations, and the best method to use will depend on the specific equation. Some common methods for solving trigonometric equations include:

• Using the unit circle
• Using the trigonometric identities
• Using the double angle formulas
• Using the half angle formulas

Factoring trigonometric equations is the process of breaking a trigonometric equation down into a product of simpler trigonometric expressions. Factoring trigonometric equations can be helpful for solving trigonometric equations, and it can also be helpful for simplifying trigonometric expressions. For example, the equation sin x + cos x = 1 can be factored as sin x + cos x = (sin x + cos x)(1) = sin x cos x + 1.

Reciprocal trigonometric equations are equations that involve the reciprocals of the trigonometric functions. Reciprocal trigonometric equations can be solved using the same methods as regular trigonometric equations. For example, the equation 1/sin x = 1/cos x can be solved as sin x = cos x.

Double angle trigonometric equations are equations that involve the double angle formulas for the trigonometric functions. Double angle trigonometric equations can be solved using the double angle formulas, or they can be solved by converting them to regular trigonometric equations. For example, the equation sin 2x = 1 can be solved using the double angle formula for sin x, which is sin 2x = 2 sin x cos x.

Half angle trigonometric equations are equations that involve the half angle formulas for the trigonometric functions. Half angle trigonometric equations can be solved using the half angle formulas, or they can be solved by converting them to regular trigonometric equations. For example, the equation tan x = √3 can be solved using the half angle formula for tan x, which is tan x = 2 tan(x/2) / 1 - tan^2(x/2).

SSC CGL Trigonometry Practice Questions

Below we have provided some Trigonometry questions for the SSC CGL exam.

Que. 1

A tower has a height of 50 m. It has an angle of elevation from two points on the ground level on its opposite sides are 30 degree and 60 degree respectively. Calculate the distance between two points.

1.) 110.97 m

2.) 107.56 m

3.) 115.47 m

4.) 120.93 m

5.) Not Attempted

Correct Option - 3

Que. 2

The value of 32cot2π/4 - 8sec2π/3 + 8cos3π/6

1.) √3

2.) 2√3

3.) 3

4.) 3√3

5.) None of the above/More than one of the above.

Correct Option - 4

Que. 3

If sec θ(cos θ + sin θ) = 2–√2, then what is the value of 2sinθ/cosθ−sinθ?

1.) 32–√2

2.) 32√32

3.) 12√12

4.) 2–√2

5.) None of the above/More than one of the above.

Correct Option - 4

Que. 4

What is the value of =(cos40∘−cos140∘)sin80∘+sin20∘−3–√?=(cos⁡40∘−cos⁡140∘)sin⁡80∘+sin⁡20∘−3?

1.) 23–√23

2.) −13√−13

3.) 13√13

4.) 3–√3

5.) None of the above/More than one of the above.

Correct Option - 2

Que. 5

Find the value of (1+tanπ/6)/(1−tanπ/6):

1.) 2 - √ 3

2.) 3 - 2√ 2

3.) 2 + √ 3

4.) 4 + √ 3

5.) None of the above/More than one of the above.

Correct Option - 3

Que. 6

Find value of tan2 30 + sin2 45.)

1.) 5656

2.) 3232

3.) 2323

4.) 2√3√23

5.) None of the above/More than one of the above.

Correct Option - 1

Que. 7

What is the value (tan30∘+cot30∘)/(sec30∘+tan30∘) * sin30∘?

1.) 2 - √3

2.) 2 + √3

3.) 2/3

4.) -2/3

5.) None of the above/More than one of the above.

Correct Option - 3

Que. 8

If 6cotθ = 5, then find the value of 6cosθ+sinθ/6cosθ−4sinθ.

1.) 1

2.) 5

3.) 0

4.) 6

5.) None of the above/More than one of the above.

Correct Option - 4

Que. 9

What is the value of 3 sin2 30° + 3535 cos2 60° − 2 sec2 45° ?

1.) −52−52

2.) −58−58

3.) −3110−3110

4.) −2517−2517

5.) None of the above/More than one of the above.

Correct Option - 3

Que. 10

2sinθ4−4sin2θ√=_______.2sin⁡�4−4sin2�=_______.

1.) 2tan θ

2.) tan θ

3.) 2cot θ

4.) cot θ

5.) None of the above/More than one of the above.

Correct Option - 2

Que. 11

If tanθ = 5/√2 and θ is an acute angle, find the value of secθ .

1.) 2

2.) 6√262

3.) 1

4.) 3232

5.) None of the above/More than one of the above.

Correct Option - 4

Que. 12

Evaluate the following expression:

3 tan245° + 2 cos 60° − 2 sin 30°

1.) 3

2.) 4

3.) 0

4.) 2

5.) None of the above/More than one of the above.

Correct Option - 1

Que. 13

What is secx/(cotx+tanx) equal to?

1.) sin x

2.) cos x

3.) tan x

4.) cot x

5.) None of the above/More than one of the above.

Correct Option - 1

Que. 14

If sin θ=15√4θ=154, then find the value of 'tan θ'.

1.) 415√415

2.) 15√2152

3.) 15−−√15

4.) 3434

5.) None of the above/More than one of the above.

Correct Option - 3

Que. 15

Find the value of sin30∘ + cos30∘/cos30∘ − sin30∘.

1.) 2 + √3

2.) 2 - √3

3.) - 2 + √3

4.) - 2 - √3

5.) None of the above/More than one of the above.

Correct Option - 1

Que. 16

If cos x = -3/5 and x lies in the third quadrant, then the value of the sin x is:

1.) 1

2.) 4545

3.) 0

4.) -4545

5.) None of the above/More than one of the above.

Correct Option - 4

Que. 17

The value of tan45∘−tan30∘/1+tan45∘tan30∘ is:

1.) 2−3–√2−3

2.) 3−2−−−−√3−2

3.) 2+3–√2+3

4.) 1

5.) None of the above/More than one of the above.

Correct Option - 1

Que. 18

If cos θ = 12/13, then the value of sinθ(1−tanθ)/tanθ(1+cosecθ) is:

1.) 25782578

2.) 3523435234

3.) 3510835108

4.) 2515625156

5.) None of the above/More than one of the above.

Correct Option - 2

Que. 19

The value of tan (13π/12) is:

1.) 4 - 3–√3

2.) 3 - 3–√3

3.) 2 - 3–√3

4.) 2 + 3–√3

5.) None of the above/More than one of the above.

Correct Option - 3

Que. 20

A vertical stick x cm long casts a shadow y cm long on the ground. At the same time, a tower casts a shadow z cm long on the ground. The height of the tower is:

1.) xz/y2

2.) xy/z

3.) yz/x

4.) xz/y

5.) None of the above/More than one of the above.

Correct Option - 4

Tips for preparing for trigonometry questions on the SSC CGL exam

Some tips for preparing for trigonometry questions on the SSC CGL exam:

1. Learn the basic trigonometric formulas. This includes the definitions of the six trigonometric functions, as well as the basic trigonometric identities.
2. Practice solving trigonometry problems. There are many different types of trigonometry problems that can be asked on the SSC CGL exam, so it is important to practice solving a variety of problems.
3. Use online resources and textbooks to learn more about trigonometry. There are many great resources available online and in libraries that can help you learn more about trigonometry.
4. Take practice exams to test your knowledge of trigonometry. This is a great way to assess your knowledge of trigonometry and identify areas where you need more practice.

Here are some additional tips:

• Focus on the most important topics. Not all trigonometry topics are equally important for the SSC CGL exam. Focus on the most important topics, such as the basic trigonometric functions, the trigonometric identities, and the double angle and half angle formulas.
• Use a variety of resources. There are many different ways to learn trigonometry. Use a variety of resources, such as textbooks, online resources, and practice exams, to help you learn the material.
• Don't be afraid to ask for help. If you are struggling with a particular topic, don't be afraid to ask for help from a tutor, teacher, or friend.

Hopefully, this article on Trigonometry Formulas for SSC CGL was informative to you. To get better preparation assistance for SSC CGL and other Govt. competitive exams, the candidates can download the Testbook App. Here you get online classes, test series and previous year's papers all in one place.