Answers

2015-07-11T08:27:18+05:30
Cos 20 × cos 40 × cos 80

Multiply and divide by sin 20

 \frac{sin 20}{sin 20} \times cos20 \times cos 40 \times cos 80\\\\=  \frac{sin 20\times cos20 }{sin 20} \times cos 40 \times cos 80\\\\= \frac{sin 40 }{2sin 20} \times cos 40 \times cos 80

(Formula used: "2 sin A cos A = sin 2A" or "sin A cos A = (sin 2A)/2 )

 =\frac{sin 40\times cos 40 }{2\ sin 20}  \times cos 80\\\\=\frac{sin 80}{2 \times 2\ sin 20}  \times cos 80\\\\=\frac{sin 80 \times cos 80}{4\ sin 20} \\\\= \frac{sin 160}{2 \times 4\ sin 20} \\\\= \frac{sin (180-20)}{8\ sin 20} \\\\= \frac{sin 20}{8\ sin 20} \\\\= \frac{1}{8}
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