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SSC CGL 2023 PYQ — Question 71

SSC CGL - 14 July 2023 - Shift 4 • Quantitative Aptitude • Q71

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Simplify the following: sin3⁡α+cos3⁡αsin⁡α+cos⁡α\frac{sin^3⁡α+ cos^3⁡α }{sin⁡ α+ cos⁡α }

 

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Correct answer: C

Explanation

The correct answer is option 3  i.e. 1 - sin α cos α.

Given that

⇒ sin3α+cos23αsin⁡α+cos⁡α\frac{sin^3α+ cos^23α }{sin⁡ α+ cos⁡α }

As we know,

sin⁡3α+cos3α\sin^3α+ cos^3α  = (sin⁡ α + cos ⁡α)(sin⁡2 α + cos2 ⁡α - sin⁡α cos⁡α)

⇒ (sin⁡ α + cos ⁡α)(sin⁡2 α + cos2 ⁡α - sin⁡α cos⁡α)/(sin⁡ α + cos ⁡α)

⇒ sin⁡2 α + cos2 ⁡α - sin⁡α cos⁡α

⇒ 1 - sin⁡α cos⁡α