Question

If $\sec 4A=cosec(A-{20}^{\circ })$, where $4A$ is an acute angle, find the value of $A$.

• A. $A={32}^{\circ }$
• B. $A={22}^{\circ }$
• C. $A={41}^{\circ }$
• D. $A={16}^{\circ }$

Answer 1

Answer: (B)

$A={22}^{\circ }$

Hence
$\sin (A-{20}^0)=\cos \left(4A\right)$
$\sin (A-{20}^0)=\sin ({90}^0-4A)$
Hence
$A-{20}^0={90}^0-4A$
$5A={110}^0$
$A={22}^0$