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# If sec 2A = cosec (A − 42°),

Question:

If $\sec 2 A=\operatorname{cosec}\left(A-42^{\circ}\right)$, where $2 A$ is an acute angles, find the value of $A$.

Solution:

Given: $\sec 2 A=\operatorname{cosec}\left(A-42^{\circ}\right)$ and $2 A$ is an acute angle

We have to find $\theta$

So we proceed as follows to calculate $\theta$

$\sec 2 A=\operatorname{cosec}\left(A-42^{\circ}\right)$

$\Rightarrow \sec 2 A=\sec \left\{90^{\circ}-\left(A-42^{\circ}\right)\right\}$

$\Rightarrow \sec 2 A=\sec \left(90^{\circ}-A+42^{\circ}\right)$

$\Rightarrow \sec 2 A=\sec \left(132^{\circ}-A\right)$

$\Rightarrow 3 A=132^{\circ}$

$\Rightarrow A=44^{\circ}$

Hence the value of $A$ is $44^{\circ}$