Question

plz answer this question​

Answer 1

$\large{\underline{\underline{\mathfrak{\green{\sf{Solution:-}}}}}}$.

$\large{\underline{\underline{\mathfrak{\pink{\sf{Given\:Here:-}}}}}}$.

✴$\red{\frac{Sin\theta\:+\:Cos\theta}{Sin\theta\:-\:Cos\theta}\:+\frac{Sin\theta\:-\:Cos\theta}{Sin\theta\:+\:Cos\theta}}$.

$\large{\underline{\underline{\mathfrak{\pink{\sf{Explanation:-}}}}}}$.

$\implies\frac{(Sin\theta\:+\:Cos\theta)}{(Sin\theta\:-\:Cos\theta)}\:+\frac{(Sin\theta\:-\:Cos\theta)}{(Sin\theta\:+\:Cos\theta)}$.

$\implies\frac{(Sin\theta\:+\:Cost theta)^2\:+\:(Sin\theta\:-\:Cos\theta)^2}{(Sin\theta\:+\:Cos\theta)\:(Sin\theta\:-\:Cos\theta)}$.

$\implies\frac{(Sin^2\theta+Cos^2\theta+2Sin\theta\:Cos\theta)\:+\:(Sin^2\theta+Cos^2\theta-2Sin\theta\:Cos\theta)}{(Sin^2\theta\:-\:Cos^2\theta)}$.

$\implies\frac{2(Sin^2\theta\:+\:Cos^2\theta)}{(Sin^2\theta\:-\:Cos^2\theta)}$.

➡We Know that .

✴$\red{(\:Sin^2\theta\:+\:Cos^2\theta\:=\:0)}$.

✴$\red{(\:Sin^2\theta\:-\:Cos^2\theta)\:=\:Cos2\theta}$.

✴$\red{(\:Cos2\theta\:=\:2Cos^2\theta\:-\:1)}$.

✴$\red{(\:Cos2\theta\:=\:1\:-\:2Sin^2\theta)}$.

➡So, Again,

We can write of above line

$\implies\frac{2}{Cos2\theta}$.

$\implies\frac{2}{(2Cos^2\theta\:-\:1)}$.

Or,

$\implies\frac{2}{(\:1\:-\:2Sin^2\theta)}$.

Here, both are We can write in answer .

So,

Final Answer will be Options Number (C).

____________________

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Answer 2

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ur offline/online

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