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SSC Selection Post 2022 PYQ — Question 54

SSC Selection Post - Graduation Level - 5 Aug 2022 - Shift 3 • Quantitative Aptitude • Q54

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If cosθ = sin(2θ) ≠ 0 , what is the value of cos4θ + sin4 θ + cos3θ + sin3θ + sin2θ + cos2θ + sinθ + cosθ?

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Correct answer: D

Explanation

The correct answer is option 4 i.e.   18+738{18 + 7 \sqrt{3} \over 8}.

Let, θ = 30°

cos4θ + sin4 θ + cos3θ + sin3θ + sin2θ + cos2θ + sinθ + cosθ

= (√3/2)4 + (1/2)4 + (√3/2)3 + (1/2)3 + 1 + √3/2 + 1/2

= 9/16 + 1/16 + (3√3)/8 + 1/8 + 1 + √3/2 + 1/2

= 5/8 + (3√3 + 1)/8 + 1 + (√3 + 1)/2

= (6 + 3√3 + 8 + 4√3 + 4)/8

= (18 + 7√3)/8