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SSC Selection Post 2019 PYQ — Question 65

SSC Selection Post - Higher Secondary Level 2019 - 15 Oct 2019 • Quantitative Aptitude • Q65

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What is the value of θ,  0° < θ < 90° , if cosθ  + sinθ = 2 \sqrt{2}?

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 45°.

Given, cosθ  + sinθ = 2 \sqrt{2} 

Squarying both sides,  (cosθ  + sinθ)2 = (2 \sqrt{2})2

⇒  cos2θ  + sin2θ + 2sinθcosθ = 2

⇒ 1 + 2sinθcosθ = 2

Now, 2sinθcosθ = sin(2θ)

⇒ 1 + sin(2θ) = 2

⇒ sin(2θ) = 1

⇒ 2θ = 90°

⇒ θ = 45°