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

Question

Question : Simplify the expression: $\frac{3 - \sin^{2} A + \cos^{2} A}{2 + 2 \cos^{2} A}$

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Answer 1

Correct Answer: 1

Solution : $\frac{\sin^{4} A + \cos^{4} A}{1 - 2 \sin^{2} A \cos^{2} A}$
Since $\sin^{2} A + \cos^{2} A = 1$ and $(\sin^{2} A + \cos^{2} A)^{2} = 1$ ,
$= \frac{\sin^{4} A + \cos^{4} A}{(\sin^{2} A + \cos^{2} A)^{2} - 2 \sin^{2} A \cos^{2} A}$
$= \frac{\sin^{4} A + \cos^{4} A}{\sin^{4} A + \cos^{4} A - 2 \sin^{2} A \cos^{2} A + 2 \sin^{2} A \cos^{2} A}$
$= \frac{\sin^{4} A + \cos^{4} A}{\sin^{4} A + \cos^{4} A}$
$= 1$
Hence, the correct answer is 1.

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Question : The given expression is equal to sin4⁡A+cos4⁡A1−2sin2⁡Acos2⁡A:Option 1: 1Option 2: –1Option 3: 0Option 4: 2

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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