Question : $\frac{\sin^4 \theta+\cos^4 \theta}{1-2 \sin^2 \theta \cos^2 \theta}=$____.
Option 1: 1
Option 2: 2
Option 3: – 1
Option 4: 0
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Correct Answer: 1
Solution :
Given:
$\frac{\sin^4 \theta+\cos^4 \theta}{1-2 \sin^2 \theta \cos^2 \theta}$
= $\frac{\sin^4\theta+\cos^4\theta+2\sin^2\theta \cos^2\theta-2 \sin^2 \theta \cos^2 \theta}{1-2 \sin^2 \theta \cos^2 \theta}$
= $\frac{(\sin^2\theta+\cos^2\theta)^2-2 \sin^2 \theta \cos^2 \theta}{1-2 \sin ^2 \theta \cos^2 \theta}$
= $\frac{1-2 \sin^2 \theta \cos^2 \theta}{1-2 \sin^2 \theta \cos^2 \theta}$ [$\because \sin^2\theta+\cos^2\theta=1$]
= $1$
Hence, the correct answer is 1.
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