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SSC CHSL 2023 PYQ — Question 30

SSC CHSL Tier II - 26 Jun 2023 - Shift 1 • Quantitative Aptitude • Q30

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What is the value of (1+ cotA + tanA )(sinA - cosA)( sin⁡Acos⁡Asin⁡3A−cos⁡3A\frac{\sin A \cos A}{\sin^3A-\cos^3A} )?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 1

= (1 + cotA + tanA )(sinA - cosA)(sin⁡Acos⁡Asin⁡3A−cos⁡3A\frac{\sin A \cos A}{\sin^3A-\cos^3A})

= (1 + cotA + tanA )(sinA - cosA) (sin⁡Acos⁡A(sin⁡A−cos⁡A)(1+sin⁡Acos⁡A)\frac{\sin A \cos A}{(\sin A-\cos A)(1+\sin A\cos A)})

= (1 + cosA/sinA + sinA/cosA)sin⁡Acos⁡A(1+sin⁡Acos⁡A)\frac{\sin A \cos A}{(1+\sin A\cos A)}

= ((sin⁡2A+cos⁡2A+sin⁡Acos⁡A)sin⁡Acos⁡A\frac{(\sin^2A+ \cos^2A+\sin A\cos A)}{\sin A \cos A})(sin⁡Acos⁡A(1+sin⁡Acos⁡A)\frac{\sin A \cos A}{(1+\sin A\cos A)})

= 1