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

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SSC CGL 2023 Tier-I Official Paper (Held On: 14 Jul 2023 Shift 1)
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  1. 75°
  2. 30°
  3.  15°
  4. 45°

Answer (Detailed Solution Below)

Option 1 : 75°
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Detailed Solution

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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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