SSC CGL Tier II 12 Apr 2015 Paper

Question : 42 of 100

Marks: +1, -0

If sin q + cos θ = 2 sin (90° – θ), then the value of cot θ is

Solution:

(3) \sin \θ+\cos \θ=√{2} \sin (90°-\θ)

⇒ \sin \θ+\cos \θ=√{2} \cos\θ

⇒ \sin\θ=√{2} \cos \θ-\cos \θ

⇒ \sin \θ=\cos \θ(√{2}-1)

⇒{\cos \θ}{\sin \θ}= {1}/{√{2}-1}

⇒ \cot\θ= {1}/{√{2}-1}

⇒ \cot \θ= {1}.{√{2}-1} ×{(√{2}+1)}/{(√{2}+1)}

= {√{2}+1}/{2-1}=√{2}+1

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