Question

Value of $\theta$ if sin $(\theta +{36}^{\circ })=\cos \theta$, where $\theta +{36}^{\circ }$ is an acute angle, is

• A. $90$${}^{\circ }$
• B. $36$${}^{\circ }$
• C. $54$${}^{\circ }$
• D. $27$${}^{\circ }$

Answer 1

The correct option is D $27$${}^{\circ }$

$\sin (\theta +{36}^0)$
$=\cos ({90}^0-\theta -{36}^0)$
$=\cos ({54}^0-\theta )$
$=\cos \theta$
Hence
$2\theta ={54}^0$
$\theta ={27}^0$