If \cos \theta=\frac{4 x}{1+4 x^{2}}, then what is the value of \sin \theta ?

Correct Answer is : 1−4x21+4x2

SSC CHSL 4 Aug 2021 Shift 1 Paper

Section: Quantitative Aptitude

Question : 52 of 100

Marks: +1, -0

\cos θ=\;{4 x}/{1+4 x^{2}}

, then what is the value of

\sin θ

Solution:

Given,

\cos θ=\;{4 x}/{1+4 x^{2}}=\;{\;\text " Base "\;}/{\;\text " Hypotenuse "\;}

∴

Perpendicular

\;\; =√{(\;\text " Hypotenuse "\;)^{2}-(\;\text " Base "\;)^{2}}

\;\; =√{(1+4 x^{2})^{2}-(4 x)^{2}}

\;\; =√{1+16 x^{4}+8 x^{2}-16 x^{2}}

\;\; =√{1+16 x^{4}-8 x^{2}}

\;\; =√{(1-4 x^{2})^{2}}=1-4 x^{2}

∴ \sin θ \;\; =\;{\;\text " Perpendicular "\;}/{\;\text " Hypotenuse "\;}=\;{1-4 x^{2}}/{1+4 x^{2}}

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