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SSC CPO 2024 PYQ — Question 103

SSC CPO - 29 June 2024 - Shift 3 • Quantitative Aptitude • Q103

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What is the value of [(sinx+siny)(siny−sinx)][(cosx+cosy)cosy−cosx)]\frac{[(sinx + siny)(siny - sinx)]}{[(cosx + cosy)cosy - cosx)]} ?

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 1.

 [(sinx+siny)(sinx−siny)][(cosx+cosy)cosy−cosx)]\frac{[(sinx + siny)(sinx - siny)]}{[(cosx + cosy)cosy - cosx)]}

⇒ [(sin2x−sin2y)][(cos2y−cos2x)]\frac{[(sin^2x - sin^2y)]}{[(cos^2y - cos^2x)]}

 ⇒ [(sin2x−sin2y)][(1−sin2y−1+sin2x)]\frac{[(sin^2x - sin^2y)]}{[(1-sin^2y - 1+sin^2x)]}

 ⇒ [(sin2x−sin2y)][(sin2x−sin2y)]\frac{[(sin^2x - sin^2y)]}{[(sin^2x - sin^2y)]}

 ⇒ 1