What is the value of ^2 +1 1+ ^2 ? - Vidyadip

Question

What is the value of $\sin^2\theta+\frac{1}{1+\tan^2\theta}?$

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Answer

$\sin^2\theta+\frac{1}{1+\tan^2\theta}=\sin^2\theta+\frac{1}{\sec^2\theta}$
$\begin{cases}\because 1+\tan^2\theta=\sec^2\theta\\ \frac{1}{\sec\theta}=\cos\theta \\ \text{and }\sin^2\theta+\cos^2\theta = 1\end{cases}$
$=\sin^2\theta+\cos^2\theta$
$=1$

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