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SSC CGL 2024 PYQ — Question 67

SSC CGL - 12 Sep 2024 - Shift 2 • Quantitative Aptitude • Q67

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Solve the following:

11 + cosθ+11 − cosθ= ?{1\over 1\ +\ cos\theta} +{1\over 1\ -\ cos\theta} = \ ?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 2cosec2θ.

According to the given question,

11 + cosθ+11 − cosθ{1\over 1\ +\ cos\theta} +{1\over 1\ -\ cos\theta}

⇒ (1−cos⁡θ)+(1+cos⁡θ)(1−cos⁡θ)(1+cos⁡θ){(1 - \cos\theta) + (1 + \cos\theta)}\over (1 - \cos\theta)(1 + \cos\theta)

⇒ 21−cos⁡2θ2 \over {1 - \cos^2\theta}

⇒ 2sin⁡2θ2\over \sin^2\theta = 2cosec2θ

Hence the required answer is 2cosec2θ.