The value of \sin 12^{\circ} \sin 48^{\circ} \sin 54^{\circ}

NIMCET 2008 Question Paper with solutions

Question : 28 of 120

Marks: +1, -0

The value of

\sin 12^{∘} \sin 48^{∘} \sin 54^{∘}

Solution:

\sin 12^{∘} \sin 48^{∘} \sin 54^{∘}

=\;{1}/{2}(2 \sin 12^{∘} \sin 48^{∘}) \sin 54^{∘}

=\;{1}/{2}[\cos (-36^{∘})-\cos 60^{∘}] \cos 36^{∘}

=\;{1}/{2}[\;{√{5}+1}/{4}-\;{1}/{2}] \;{√{5}+1}/{4}

=\;{1}/{2}[\;{√{5}+1-2}/{4}] \;{√{5}+1}/{4}

=\;{1}/{32}(5-1)=\;{1}/{8}=(\;{1}/{2})^{3}=\sin ^{3} 30^{∘}

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