Question

If $sec\left(4A\right)=\cos ec\left(A-20°\right)$, where $4A$ is an acute angle, find the value of $A$.

Answer 1

Find the required value.

An angle that is less than $90°$ is called an acute angle.

Since, $4A$ is an acute angle.

Therefore, $4A<90°$

$\Rightarrow A<22.5°$

Write $sec\left(4A\right)$ in terms of cosecant as follows:

$sec\left(4A\right)=\cos ec(90°-4A)...1$

Also, $sec\left(4A\right)=\cos ec\left(A-20°\right)...2$ {Given}

Compare equation $1$ and equation $2$.

$$\begin{gathered} A-20°=90°-4A \\ \Rightarrow 5A=110° \\ \Rightarrow A=22° \end{gathered}$$

Which also satisfies $A<22.5°$.

Hence, the value of $A$ is $22°$.