Question : If $\cos^2x+\cos^4x=1$, then $\tan^2x+\tan^4x$?
Option 1: $0$
Option 2: $1$
Option 3: $2 \tan^2x$
Option 4: $2\tan^4x$
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Correct Answer: $1$
Solution : $\cos^2x+\cos^4x=1$ ⇒ $\cos^4x = 1 - \cos^2x$ ⇒ $\cos^4x = \sin^2x$ [Using $1-\cos^2x=\sin^2x$] ⇒ $\cos^2x\times \cos^2x=\sin^2x$ ⇒ $\tan^2x=\cos^2x$ --------(i) On squaring, $\tan^4x=\cos^4x$ ------(ii) ⇒ $\tan^2x+\tan^4x = \cos^2x+\cos^4x$ ⇒ $\tan^2x+\tan^4x=1$ Hence, the correct answer is $1$.
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