Question : The given expression is equal to $\frac{\sin^4 A+\cos^4 A}{1-2 \sin^2 A \cos^2 A}$:
Option 1: 1
Option 2: –1
Option 3: 0
Option 4: 2
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Correct Answer: 1
Solution :
$\frac{\sin^4 A+\cos^4 A}{1-2 \sin^2 A \cos^2 A}$
Since $\sin^2A+\cos^2 A=1$ and $(\sin^2A+\cos^2 A)^2=1$,
$=\frac{\sin^4 A+\cos^4 A}{(\sin^2A+\cos^2 A)^2 -2 \sin^2 A \cos^2 A}$
$= \frac{\sin^4 A+\cos^4 A}{\sin^4A+\cos^4 A -2 \sin^2 A \cos^2 A +2 \sin^2 A \cos^2 A}$
$=\frac{\sin^4 A+\cos^4 A}{\sin^4A+\cos^4 A }$
$=1$
Hence, the correct answer is 1.
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