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SSC CGL 2023 PYQ — Question 55

SSC CGL - 26 July 2023 - Shift 3 • Quantitative Aptitude • Q55

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Find the value of cos⁡215∘−sin⁡215∘cos⁡2145∘+sin⁡2145∘\frac{\cos^2 15^\circ - \sin^2 15^\circ}{\cos^2 145^\circ + \sin^2 145^\circ}

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 32\frac{\sqrt{3}}{2}.

Given that

cos⁡215∘−sin⁡215∘cos⁡2145∘+sin⁡2145∘\frac{\cos^2 15^\circ - \sin^2 15^\circ}{\cos^2 145^\circ + \sin^2 145^\circ}

We know that

cos2A = cos⁡2A−sin⁡2A\cos^2 A - \sin^2 A

Also, cos⁡2A+sin⁡2A=1\cos^2 A + \sin^2 A = 1

Hence, cos⁡215∘−sin⁡215∘cos⁡2145∘+sin⁡2145∘\frac{\cos^2 15^\circ - \sin^2 15^\circ}{\cos^2 145^\circ + \sin^2 145^\circ} = cos (2 × 15) = cos 30º = 32\frac{\sqrt{3}}{2}