If sin (A + B) = cos (A + B), what is the value of tan A?

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SSC CGL 2022 Tier-I Official Paper (Held On : 02 Dec 2022 Shift 1)
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  1. \(\frac{{1 - \tan B}}{{1 + \tan B}}\)
  2. \(\frac{{1 + \tan B}}{{1 - \tan B}}\)
  3. \(\frac{{1 + \sec B}}{{1 - \sec B}}\)
  4. \(\frac{{1 - Cosec \ B}}{{1 + cosec\ B}}\)

Answer (Detailed Solution Below)

Option 1 : \(\frac{{1 - \tan B}}{{1 + \tan B}}\)
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PYST 1: SSC CGL - English (Held On : 11 April 2022 Shift 1)
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Detailed Solution

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Given:

sin (A + B) = cos (A + B)

Formula used:

sin (A + B) = sin A cos B + cos A sin B

cos (A + B) =  cos A cos B - sin A sin B

Calculation:

sin (A + B) = cos (A + B)

sin A cos B + cos A sin B = cos A cos B - sin A sin B

sin A cos B + sin A sin B = cos A cos B - cos A sin B

sin A(cos B + sin B) = cos A (cos B - sin B)

sin A/cos A = (cos B - sin B)/(cos B + sin B)

sin A/cos A = (1 - sin B/cos B)/(1 + sin B/cos B)

tan A = (1 - tan B)/(1 + tan B)

∴ Option 1 is the correct answer.

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