If sin (a + b) = 1 and cos (a - b) = \(\frac{1}{2} \), then find a.

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 14 Jul 2023 Shift 1)

Answer 1

Given:

sin(A + B) = 1 and cos(A - B) = 1/2

Formula used:

sin90° = 1

cos60° = 1/2

Calculation:

sin(A + B) = 1

⇒ sin(A + B) = sin90°

⇒ A + B = 90° ....(1)

Again,

cos(A – B) = 1/2

⇒ cos(A – B) = cos60°

⇒ A – B = 60° .....(2)

Adding equation (1) and (2), we get

⇒ A + B + A – B = (90° + 60°)

⇒ 2A = 150°

⇒ A = (150/2)

⇒ A = 75°

The value of a is 75°.

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