(solved)Question 23 SSC-CGL 2020 March 3 Shift 2

If sinθ = 1/4, then the value of 8(cosθ + cotθ) is?
(Rev. 31-Oct-2024)

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Question 23
SSC-CGL 2020 Mar 3 Shift 2

If sinθ = 1/4, then the value of 8(cosθ + cotθ) is?

Solution in Detail

Given sinθ=14\displaystyle \sin \theta = \frac 14

H=4,P=1\displaystyle \therefore H = 4, P = 1

so B=421=15\displaystyle B = \sqrt{4^2 - 1} = \sqrt {15}

    cosθ=BH=154\displaystyle \implies \cos \theta = \frac BH = \frac{\sqrt {15}}{4}

cotθ=BP=151=15\displaystyle \cot \theta = \frac BP= \frac{\sqrt {15}}{1} = \sqrt {15}

8(cosθ+cotθ)\displaystyle \therefore 8(\cos \theta + \cot \theta)

=8(154+15)\displaystyle = 8\bigg(\frac{\sqrt {15}}{4} + \sqrt {15}\bigg)

=1015Ans\displaystyle =10\sqrt{15}\:\underline{Ans}

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