Q63 / 160 · AP EAMCET 2022 (04 Jul Shift 2) · Mathematics

$1 + \sec^{2} x \sin^{2} x =$

A
$\sin 2 x$
B
$\sin^{2} x$
C
$\tan^{2} x$
Correct answer
D
$\sec^{2} x$

Solution

Let
$f (x) = 1 + \sec^{2} x \sin^{2} x$
$\Rightarrow f (x) = 1 + (\frac{\sin^{2} x}{\cos^{2} x})$
$[∵ \sec x = \frac{1}{\cos x}]$
$\Rightarrow f (x) = 1 + \tan^{2} x$
$[∵ \tan x = \frac{\sin x}{\cos x}]$
$\Rightarrow f (x) = \sec^{2} x$

Hence, the correct answer is option: 'D'.

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