Question : Simplify the expression: $\frac{3-\operatorname{\sin}^2 A+\operatorname{\cos}^2 A}{2+2 \operatorname{\cos}^2 A}$
Option 1: 1
Option 2: 0
Option 3: –1
Option 4: 2
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Correct Answer: 1
Solution :
$\frac{3-\operatorname{\sin}^2 A+\operatorname{\cos}^2 A}{2+2 \operatorname{\cos}^2 A}$
$=\frac{1-\operatorname{\sin}^2 A+2+\operatorname{\cos}^2 A}{2+2 \operatorname{\cos}^2 A}$
$=\frac{\operatorname{\cos}^2 A+2+\operatorname{\cos}^2 A}{2+2 \operatorname{\cos}^2 A}$ [$\because\cos^2 A=1-\sin^2 A$]
$=\frac{2+2\operatorname{\cos}^2 A}{2+2 \operatorname{\cos}^2 A}$
$=1$
Hence, the correct answer is 1.
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