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SSC CGL 2023 PYQ — Question 71

SSC CGL - 18 July 2023 - Shift 2 • Quantitative Aptitude • Q71

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The value of (1sinθ+1tanθ)(1sinθ−1tanθ)(\frac{1}{sin\theta} + \frac{1}{tan\theta}) (\frac{1}{sin\theta} - \frac{1}{tan\theta}) is:

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 1.

The value of (1sinθ+1tanθ)(1sinθ−1tanθ)(\frac{1}{sin\theta} + \frac{1}{tan\theta}) (\frac{1}{sin\theta} - \frac{1}{tan\theta}) 

⇒ (1sinθ+1tanθ)(1sinθ−1tanθ)(\frac{1}{sin\theta} + \frac{1}{tan\theta}) (\frac{1}{sin\theta} - \frac{1}{tan\theta})

⇒ (1sinθ+cosθsinθ)(1sinθ−cosθsinθ)(\frac{1}{sin\theta} + \frac{cos\theta}{sin\theta}) (\frac{1}{sin\theta} - \frac{cos\theta}{sin\theta})

⇒ (1+cosθsinθ)(1−cosθsinθ)(\frac{1 + cos\theta }{sin\theta}) (\frac{1 - cos\theta}{sin\theta})

⇒ (1−cos2θsin2θ)(\frac{1 - cos^2\theta }{sin^2\theta})

⇒ (sin2θsin2θ)(\frac{ sin^2\theta }{sin^2\theta})

⇒ 1