The value of \sin 10^\circ\sin 50^\circ\sin 70^\circ is

NIMCET 2020 Question Paper with solutions

Question : 43 of 120

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The value of

\sin 10°\sin 50°\sin 70°

Solution:

\sin 10°\sin 50°\sin 70°

⇒\cos 80°\cos40°\cos20°

⇒{2\sin20\cos20\cos40\cos80}/{\sin20}⇒{\sin40\cos40\cos80}/{2\sin20}

⇒{2\sin40\cos40\cos80}/{2.2\sin20}⇒{\sin80\cos80}/{4\sin20}

⇒{2\sin80\cos80}/{2'4\sin20}⇒{\sin160}/{8\sin20}

⇒{\sin20}/{8\sin20}⇒1/8

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