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SSC CHSL 2021 PYQ — Question 71

SSC CHSL - 19 April 2021 - Shift 3 • Quantitative Aptitude • Q71

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If sinθ+cosθsinθ−cosθ=3,{{sin\theta+cos\theta} \over sin\theta-cos\theta}=3,then the value of sin4θ−cos4θ{{sin^4\theta-cos^4\theta}} is equal to:

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Correct answer: B

Explanation

 The correct answer is Option 2 i.e. 35{{3} \over 5}.

sinθ+cosθsinθ−cosθ=3{{sin\theta+cos\theta} \over sin\theta-cos\theta}=3

sinθ + cosθ  = 3 × (sinθ - cosθ)

⇒ 2 sinθ = 4 cosθ 

⇒ tanθ = 2/1 = P/B

P2 + B2 = H2

⇒ 4 + 1 = H2

⇒ H = 5\sqrt5

The  value of sin4θ−cos4θ{{sin^4\theta-cos^4\theta}} = (25)4−(15)4(\frac{2}{\sqrt5})^4-(\frac{1}{\sqrt5})^4 = 15/25 = 35{{3} \over 5}