Question

If $sec5A=cosec(A+{36}^{\circ })$ where 5A is an acute angle, find the value of A.

Answer 1

$sec5A=cosec(A+{36}^{\circ })$

$\Rightarrow sec5A=sec({90}^{\circ }-(A+{36}^{\circ }\left)\right)$

$\Rightarrow sec5A=sec({54}^{\circ }-A)$

$\Rightarrow 5A={54}^{\circ }-A\Rightarrow 6A={54}^{\circ }\Rightarrow A=9^{\circ }$