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SSC CPO 2024 PYQ — Question 103

SSC CPO - 29 June 2024 - Shift 1 • Quantitative Aptitude • Q103

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The value of (cosecθ - sinθ)(secθ - cosθ)(tanθ + cotθ) is :

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Correct answer: A

Explanation

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

According to the given question,

(cosecθ - sinθ)(secθ - cosθ)(tanθ + cotθ)

⇒ (1sin⁡θ−sin⁡θ)(1cos⁡θ−cosθ)(sin⁡θcos⁡θ+cos⁡θsin⁡θ)({1 \over \sin\theta} - {\sin\theta})({1\over \cos\theta} - cos\theta)({\sin\theta \over \cos\theta} + {\cos\theta \over \sin\theta})

⇒ (1−sin⁡2θsin⁡θ)(1−cos⁡2θcos⁡θ)(sin⁡2θ+cos⁡2θ)sin⁡θcos⁡θ({{1 - \sin^2\theta} \over \sin\theta})({{1 - \cos^2\theta} \over \cos\theta}){({\sin^2\theta + \cos^2\theta})\over {\sin\theta \cos\theta}}

⇒ (cos⁡2θsin⁡θ)(sin⁡2θcos⁡θ)(1sin⁡θcos⁡θ)({{\cos^2\theta} \over \sin\theta})({{\sin^2\theta} \over \cos\theta})({{1}\over {\sin\theta \cos\theta}}) = 1

Hence the required answer is 1.