Question

If sin (x + y) = cos (x - y), then the value of cos² x is:
1. 3
2. 5
3. 1 / 4
4. 1 / 2

Answer 1

Correct Answer - Option 4 : 1 / 2

GIVEN:

sin (x + y) = cos (x - y)

CONCEPT USED:

sinθ₁ = cosθ₂ , when θ₁ + θ₂ = 90° 

CALCULATION:

sin (x + y) = cos (x - y)

⇒ (x + y) + (x - y) = 90° 

⇒ 2x = 90° 

⇒ x = 45° 

⇒ cos²x = cos²45° 

⇒ (1/√2)² 

⇒ 1/2

∴ cos2x  = 1/2