Question

sin (45° + θ) – cos (45° – θ) is equal to

(A) 0 (B) sin θ (C) 1 (D) 2 cosec θ (E) None of these

Answer 1

Correct option is : (A) 0

Answer 2

The correct option is (A) 0.

sin (45° + θ) - cos (45° - θ)

As we know that

cos (90° - A) = sin A

cos (45° - θ) = cos (90° - (45° - θ))

= cos(90° - 45° + θ)

= sin(45°+ θ)

sin(45°+ θ) - cos(45°- θ) 

= sin(45°+ θ) - sin(45°+ θ)

= 0