Question

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$\huge\rm \color{fuchsia} \dfrac{1+cosec \ A}{cosec \ A}}$ =$\huge \rm \color{lime} \dfrac{sin^2 \ A}{1-sin \ A}}$
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Answer 1

Answer:

• A = 45°

Step-by-step explanation:

$\begin{lgathered}\frac{1+\csc A}{\csc A}=\frac{\sin^2 A}{1-\sin A}\\\\\implies \frac{1}{\csc A}+\frac{\csc A}{\csc A}=\frac{\sin^2 A}{1-\sin A}\\\\\implies \sin A+1=\frac{\sin^2 A}{1-\sin A}\\\\\implies (1-\sin A)(1+\sin A)=\sin^2 A\\\implies 1-\sin^2 A= \sin^2A\\\implies 1=2\sin^2A\\\implies \sin^2A=\frac{1}{2}\\\\\implies \sin A=\frac{1}{\sqrt{2}}\\\\\implies \sin A = \sin 45\\\\\implies A=\sin^{-1}\sin 45\\\implies A = 45\end{lgathered}$

Hence, A = 45°

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Answer 2

Answer:

A = 45

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