If sin 3A = cos (A - 30), where 3A and (A - 30) are acute angles, find the value of (sin 2A + cos 2A)

Question

Question

Answer 1

Concept:

cos(90° - x) = sin x

Calculation:

Given:

sin 3A = cos (A - 30) & (sin 2A + cos 2A) = ?

sin 3A = cos (90° - (A - 30))

sin 3A = sin (90° - A + 30))

sin 3A = sin (120° - A)

3A = 120° - A

A = 30°

Now,

(sin 2A + cos 2A) = sin(2 × 30) + cos(2 × 30)

= sin 60° + cos 60°

= \(\frac {\sqrt 3}{2}+\frac 1 2 \)

= \( \frac {\sqrt 3 \ +\ 1}{2}\)