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SSC CGL 2022 PYQ — Question 65

SSC CGL - 02 Dec 2022 - Shift 4 • Quantitative Aptitude • Q65

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If 1−cos⁡θsinθ{1 -\cosθ \over sinθ}=15{1 \over 5} , then what will be the value of  1+cosθsinθ1 + cosθ \over sin θ ?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 5

Given:

  1−cos⁡θsinθ{1 -\cosθ \over sinθ}=15{1 \over 5} 

Concept Used:

sin2θ=1−cos2θsin^2 \theta = 1 - cos^2\theta   ...(i)

Explanation:

  1−cos⁡θsinθ{1 -\cosθ \over sinθ}=15{1 \over 5} 

Multiplying (1+cos⁡θ)(1 + \cos\theta) in both numerator and denominator, we get

⇒ (1−cos⁡θ)(1+cos⁡θ)sin⁡θ(1+cos⁡θ)=15{(1 - \cos\theta)(1 + \cos\theta) \over \sin\theta(1 + \cos\theta)} = {1 \over 5}

⇒ (1−cos⁡2θ)sin⁡θ(1+cos⁡θ)=15{(1 - \cos^2\theta) \over \sin\theta(1 + \cos\theta)} = {1 \over 5}

⇒ sin⁡θ1+cos⁡θ=15{\sin\theta \over 1 +\cos\theta }= { 1\over 5}

⇒  1+cosθsinθ1 + cosθ \over sin θ = 5.

Hence the value of 1+cosθsinθ1 + cosθ \over sin θ is 5.