Without using calculator, evaluate: Cos100cos120cos140cos160 ?

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Without using calculator, evaluate: Cos100cos120cos140cos160 ?

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Answer 1 · 2017-05-15T10:51:27

$cos 100 cos 120 cos 140 cos 160$ $cos100cos120cos140cos160$

$= cos (180 - 80) cos (180 - 60) cos (180 - 40) cos (180 - 20)$ $=cos(180-80)cos(180-60)cos(180-40)cos(180-20)$

$= (- cos 80) (- cos 60) (- cos 40) (- cos 20)$ $=(-cos80)(-cos60)(-cos40)(-cos20)$

$= cos 20 \times cos 40 \times cos 80 cos 60$ $=cos20xxcos40xxcos80cos60$

$= \frac{1}{8 sin 20} \times 4 \cdot 2 sin 20 \times cos 20 \times cos 40 \times cos 80 cos 60$ $=1/(8sin20)xx4*2sin20xxcos20xxcos40xxcos80cos60$

$= \frac{1}{8 sin 20} \times 2 \cdot 2 sin 40 \times cos 40 \times cos 80 cos 60$ $=1/(8sin20)xx2*2sin40xxcos40xxcos80cos60$

$= \frac{1}{8 sin 20} \times 2 sin 80 \times cos 80 cos 60$ $=1/(8sin20)xx2sin80xxcos80cos60$
$= \frac{1}{8 sin 20} \times sin 160 cos 60$ $=1/(8sin20)xxsin160cos60$

$= \frac{1}{8 sin 20} \times sin (180 - 20) \times \frac{1}{2}$ $=1/(8sin20)xxsin(180-20)xx1/2$

$= \frac{1}{16 sin 20} \times sin 20 = \frac{1}{16}$ $=1/(16sin20)xxsin20=1/16$

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Without using calculator, evaluate: Cos100cos120cos140cos160 ?

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