If \sin (\\theta+30^\circ )= {3}/\sqrt{12}, then the value of \cos ^{2} \\theta is

SSC CGL Tier II 12 Apr 2015 Paper

Question : 46 of 100

Marks: +1, -0

\sin (\θ+30° )= {3}/{√{12}},

then the value of

\cos ^{2} \θ

Solution:

\sin (\θ+30° )= {3}/{√{12}}

=3/{2√3}=√3/2

⇒ sin (θ + 30°) = sin 60°
⇒ θ + 30° = 60°
⇒ θ = 60 – 30 = 30°

∴\cos ^{2} \θ=\cos^2 30°

= ( {√{3}}/{2} )^{2}= {3}/{4}

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