Question

If sec 5 A = cosec (A − 36) and 5 A is an acute angle, find the value of A.

Answer 1

$$\begin{gathered} \text{Given: sec5}A=\cos ec(A-{36}^0) \\ \text{=> cosec}({90}^0-5A)=\cos ec(A-{36}^0)[\because \cos ec({90}^0-\theta )=\sec \theta ] \\ \text{=>}{90}^0-5A=A-{36}^0 \\ \text{=>6}A={90}^0+{36}^0 \\ \text{=> 6}A={126}^0 \\ \text{=>}A={21}^0 \end{gathered}$$