Question : If $2\tan^2A+4\cos^4A=3$, then the possible value of $A$ is:
Option 1: 45°
Option 2: 60°
Option 3: 0°
Option 4: 30°
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Correct Answer: 45°
Solution :
Given: $2\tan^2A+4\cos^4A=3$
Take $A = 45°$ then,
$2\tan^2A+4\cos^4A=2(1)^2+4(\frac{1}{\sqrt2})^4 = 2 + 1 = 3$
So, $A = 45°$ satisfies the given equation.
Hence, the correct answer is 45°.
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