Question

If $\sec 5A=\text{cosec}(A-30)$, where $\angle A$ is acute angle, then $\angle A=$ ____

• A. ${35}^{\circ }$
• B. ${25}^{\circ }$
• C. ${20}^{\circ }$
• D. ${27}^{\circ }$

Answer 1

Answer: (C)

${20}^{\circ }$

Given, $\sec 5A=\text{cosec}(A-{30}^{\circ })$

We know $\text{cosec}({90}^{\circ }-5A)=\text{cosec}(A-{30}^{\circ })$
$\Rightarrow {90}^{\circ }-5A=A-{30}^{\circ }$

$\Rightarrow 6A={120}^{\circ }$
So, $\angle A={20}^{\circ }$