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SSC CGL 2018 PYQ — Question 45

SSC CGL Tier II Quant - 09/03/2018 • Quantitative Aptitude • Q45

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What is the value of cot(90 − x) sin4(90 − x) + cot(180 − x) sin4(180 − x) ?

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Correct answer: D

Explanation

The correct answer is Option 4 i.e. 1/4 × Sin4x

Application

cot(90 − x) sin4(90 − x) + cot(180 − x) sin4(180 − x)

= Tan x Cos4x – Cot x Sin4x

= (Sin x/Cos x) Cos4x – (Cos x/Sin x) Sin4x

= Sin x Cos3x – Cos x Sin3x

= Sinx Cos x (Cos2x – Sin2x)

= 1/2 × Sin2x × Cos2x

= 1/4 × Sin4x