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SSC CHSL 2023 PYQ — Question 54

SSC CHSL - 04 Aug 2023 - Shift 1 • Quantitative Aptitude • Q54

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Simplify the expression; 3−sin2+cos2A2+2cos2A\frac{3-sin^2+cos^2A}{2+2cos^2A}

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Correct answer: A

Explanation

The correct answer is Option 1 i.e 1.

3−sin2A+cos2A2+2cos2A\frac{3-sin^2A+cos^2A}{2+2cos^2A}

We know that, sin2A + cos2A = 1

⇒ 2+1−sin2A+cos2A2+2cos2A\frac{2 + 1 - sin^2A+cos^2A}{2+2cos^2A}

⇒ 2+sin2A+cos2A−sin2A+cos2A2+2cos2A\frac{2 + sin^2A + cos^2A - sin^2A+cos^2A}{2+2cos^2A}

⇒ 2+2cos2A2+2cos2A\frac{2 + 2cos^2A }{2+2cos^2A} = 1