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प्रश्न
If \[f\left( x \right) = \frac{\sin^4 x + \cos^2 x}{\sin^2 x + \cos^4 x}\] for x ∈ R, then f (2002) =
पर्याय
(a) 1
(b) 2
(c) 3
(d) 4
उत्तर
(a) 1
Given:
\[f\left( x \right) = \frac{\sin^4 x + \cos^2 x}{\sin^2 x + \cos^4 x}\] On dividing the numerator and denominator by \[\cos^4 x\]\ , we get \[f\left( x \right) = \frac{\tan^4 x + \sec^2 x}{1 + \tan^2 x \sec^2 x} = \frac{1 + \tan^4 x + \tan^2 x}{1 + \tan^2 x\left( 1 + \tan^2 x \right)} = \frac{1 + \tan^4 x + \tan^2 x}{1 + \tan^4 x + \tan^2 x} = 1\] (For every x ∈ R)
For x = 2002, we have
f (2002) = 1
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