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SSC CHSL 2020 PYQ — Question 69

SSC CHSL - 14th October 2020 - Shift 3 • Quantitative Aptitude • Q69

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If Sinθ – cosθ = 7/17, then find the value of sinθ + cosθ.

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Correct answer: B

Explanation

The correct answer is option 2 i.e 23/17

⇒ Sinθ – cosθ = 7/17

 Squaring both the sides,

⇒ (Sinθ – cosθ)2 = (7/17)2

⇒ (Sinθ – cosθ)2 = Sin2θ + Cos2θ - 2SinθCosθ

⇒ 2SinθCosθ = 1 - (7/17)2

We need to find out sinθ + cosθ

⇒ (sinθ + cosθ)2 = Sin2θ + Cos2θ + 2SinθCosθ

⇒ (sinθ + cosθ)2 = 1 + (1 - (7/17)2)

⇒ (sinθ + cosθ)2 = 529 / 289

⇒ sinθ + cosθ = 23 / 17