Question

Q.15. The value of [sin^ theta + 1/ 1 + tan^ theta] = _________.
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Answer 1

Solution:-

$\implies \: sin {}^{2} + \frac{1}{1 + tan {}^{2 \:}\theta }$

$\begin{cases} \: since \: we \: know - \: 1 + {tan {}^{2}\theta = sec {}^{2}\theta } \end{cases}$

Applying this trigonometric identity we'll get,

$\implies \: sin {}^{2}\theta \: + \frac{1}{sec {}^{2}\theta }$

Since we know 1/sec² θ= cos²θ

$\implies \: sin {}^{2} \theta \: + \: cos {}^{2} \theta = 1$

Therefore, our required answer is 1.

Answer 2

The value of [sin^ theta + 1/ 1 + tan^ theta] = 1

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