Question

(1-sin^2 theta) sec^2 theta = 1

Answer 1

$\huge{\bigstar}}$$\huge{\boxed{\red{\mathfrak{Answer}}}}$$\huge{\bigstar}}$

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$\mathtt{\underline{\underline{\green{Given:}}}}$

$(1 - {sin}^{2} x)( {sec}^{2} x) = 1$

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$\mathtt{\underline{\underline{\blue{Solution:}}}}$

LHS:

We know that ,

$\boxed{1 - {sin}^{2} x = {cos}^{2} x}$

So,

$= ({cos}^{2} x)( {sec}^{2} x)$

$\boxed{Sec\:x = \frac{1}{cos\:x}}$

$= {cos}^{2} x \times \frac{1}{ {cos}^{2} x} \\ = 1$

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$\huge{\mathtt{\underline{\underline{\purple{Hence\:Proved}}}}}$