Question

Consider the expression sin 0 + cos( 90° - 0) + cos 0 + sin( 90° - 0). For any angle 0, which of the following is equivalent to the expression above? (A) O (B) 2 sin 0 (C) 2 cos 0(D) 2 (sin 0 + cose)

Answer 1

Given data:

The given expression is sinθ+cos(90-θ)+cosθ+sin(90-θ).

cos(90-θ)=sinθ, and sin(90-θ)=cosθ, so the above expression can be written as,

sinθ+sinθ+cosθ+cosθ=2sinθ+2cosθ

=2(sinθ+cosθ)

Thus, option D) is correct.