Given 38^ (90^ -2 A )=1 , Find the value of A - Vidyadip

Question

$
\text { Given } \cos 38^{\circ} \sec \left(90^{\circ}-2 A\right)=1 \text {, Find the value of } \angle \mathrm{A}
$

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Answer

$
\begin{aligned}
& \cos 38^{\circ} \sec \left(90^{\circ}-2 A\right)=1 \\
& \Rightarrow \cos 38^{\circ} \cos e c 2 A=1 \\
& \Rightarrow \cos 38^{\circ}\left(\frac{1}{\sin 2 A}\right)=1 \\
& \Rightarrow \sin 2 A=\cos \left(90-52^{\circ}\right) \\
& \Rightarrow \sin 2 A=\sin 52^{\circ} \\
& \Rightarrow 2 A=52^{\circ} \\
& \Rightarrow A=26^{\circ}
\end{aligned}
$

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