Question

(cos²37° − sin²53°) = ?
(a) $\frac{1}{3}$
(b) $\frac{2}{\sqrt{3}}$
(c) 1
(d) 0

Answer 1

$$\begin{gathered} \text{(d) 0} \\ \text{We have:} \\ ({\cos }^2{37}^0-{\sin }^2{53}^0) \\ ={\cos }^2({90}^0-{53}^0)-{\sin }^2{53}^0 \\ ={\sin }^2{53}^0-{\sin }^2{53}^0[\because \cos ({90}^0-\theta )=\sin \theta ] \\ =0 \end{gathered}$$