Prove that --
cos20°cos40° cos60° cos80° =1

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Solution

Solution is sent by previous ESE is correct. Answer is 1/16. You have to coscos formulas repeatedly by arranging angles in proper manner. & If this would have been an MCQ first thing you have to do is check options. Because range of cosine function from 0 to 90° is 1 to 0. So obviously for all angles between them answer will lie between 1 & O. & If you are multiplying four numbers which are less than 1 & greater than zero obviously resultant will be less than 1. So answer cannot be 1 it's 1/16. & If it's one then there has to be some correction in question or some sort of printing mistake.

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c o s 20^{\circ} c o s 40^{\circ} c o s 60^{\circ} c o s 80^{\circ} = \frac{1}{16}

cos 20^{\circ} \cdot cos 40^{\circ} \cdot cos 60^{\circ} \cdot cos 80^{\circ} = . . . . .

cos 20^{\circ} . cos 40^{\circ} . cos 60^{\circ} . cos 80^{\circ}

{c o s 20}^{\circ} c o s 40^{\circ} {c o s 60}^{\circ} c o s 80^{o} = \frac{1}{16}

α

β

a c o s θ + b s i n θ = c

s i n (α + β) = \frac{2 a b}{a^{2} + b^{2}}

c o s 20^{\circ} c o s 40^{\circ} c o s 60^{\circ} c o s 80^{\circ} = \frac{1}{16}

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