Question

cos (40° + θ) − sin (50° − θ) = ?
(a) 1
(b) 0
(c) sin 2θ
(d) None of these

Answer 1

$$\begin{gathered} (b)\; 0 \\ \text{We have:} \\ [\cos ({40}^0+\theta )-\sin ({50}^0-\theta )] \\ =[\cos \{{90}^0-({50}^0-\theta )\}-\sin ({50}^0-\theta )] \\ \text{=}[\sin ({50}^0-\theta )-\sin ({50}^0-\theta )][\because \cos ({90}^0-\theta )=\sin \theta ] \\ =0 \end{gathered}$$