Question : Find the value of the following expression $2(\tan ^2 A \cos ^2 A+\cos ^2 A)$.
Option 1: 4
Option 2: 1
Option 3: 3
Option 4: 2
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Correct Answer: 2
Solution :
$2(\tan ^2 A \cos ^2 A+\cos ^2 A)$
= $2\cos ^2 A(\tan ^2 A + 1)$
= $2\cos ^2 A×\operatorname{sec}^2A$
= $2\cos ^2 A×\frac{1}{\cos^2A}$
= $2$
Hence, the correct answer is 2.
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