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SSC CHSL 2023 PYQ — Question 66

SSC CHSL - 09 March 2023 - Shift 3 • Quantitative Aptitude • Q66

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What is the value of (1 + tanθ - secθ)(1 + cotθ  + cosecθ)?

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Correct answer: D

Explanation

The correct answer is Option 4 i.e. 2.

(1 + tanθ - secθ)(1 + cotθ  + cosecθ)

=(1+sin⁡θcos⁡θ−1cos⁡θ)(1+cos⁡θsin⁡θ+1sin⁡θ)= \left(1 + \frac{\sin\theta}{\cos\theta} - \frac{1}{\cos\theta}\right) \left(1 + \frac{\cos\theta}{\sin\theta} + \frac{1}{\sin\theta}\right)

=(cos⁡θ+sin⁡θ−1cos⁡θ)(sin⁡θ+cos⁡θ+1sin⁡θ)= \left(\frac{\cos\theta + \sin\theta - 1}{\cos\theta}\right) \left(\frac{\sin\theta + \cos\theta + 1}{\sin\theta}\right)

=(cos⁡θ+sin⁡θ−1)(cos⁡θ+sin⁡θ+1)cos⁡θsin⁡θ= \frac{(\cos\theta + \sin\theta - 1)(\cos\theta + \sin\theta + 1)}{\cos\theta \sin\theta}

=1+2sin⁡θcos⁡θ−1cos⁡θsin⁡θ= \frac{1 + 2\sin\theta\cos\theta - 1}{\cos\theta \sin\theta}

= (2sinθ cosθ)/(sinθ cosθ)

= 2