Question

If $\sin (7\varphi -9^o)=\cos 2\varphi$, find a value of $\varphi$

Answer 1

Consider the given expression,

$\sin (7\varphi -9)=\cos \varphi$

$\because \cos ({90}^0-\theta )=\sin \theta$

$\therefore \sin (7\varphi -9)=\sin ({90}^0-\varphi )$

$7\varphi -9={90}^0-\varphi$

$8\varphi =81$

$\varphi =\frac{81}{8}$

Hence, this is the answer.