(D) Given expression: $f(x) = 1 + \sec ^2 x \sin ^2 x$ Since $\sec x = \frac{1}{\cos x}$,we have $\sec ^2 x = \frac{1}{\cos ^2 x}$. Substituting this

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(D) Given expression: $f(x) = 1 + \sec ^2 x \sin ^2 x$ Since $\sec x = \frac{1}{\cos x}$,we have $\sec ^2 x = \frac{1}{\cos ^2 x}$. Substituting this into the expression: $f(x) = 1 + \frac{\sin ^2 x}{\cos ^2 x}$ Since $\tan x = \frac{\sin x}{\cos x}$,we have $\tan ^2 x = \frac{\sin ^2 x}{\cos ^2 x}$. Therefore,$f(x) = 1 + \tan ^2 x$ Using the identity $1 + \tan ^2 x = \sec ^2 x$,we get $f(x) = \sec ^2 x$.

Class 11 Mathematics Trigonometrical Ratios, Functions and Identities Fundamental trigonometrical ratios and functions, Trigonometrical ratio of allied angles

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

AP EAMCET 2022 All AP EAMCET

A
$\sin 2 x$
B
$\sin ^2 x$
C
$\tan ^2 x$
D
$\sec ^2 x$

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Trigonometrical Ratios, Functions and Identities

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Fundamental trigonometrical ratios and functions, Trigonometrical ratio of allied angles

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