cos 40° cos 100° cos 160°
=1/8
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Answer:
Step-by-step explanation:
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AS THE QUESTION IS TO PROVE
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Given, cos40°×cos80°×cos160°.....
It can be written as,.
cos40×cos(120-40)×cos(120+40)
cos40×[cos120×cos40+sin120×sin40]×[cos120×cos40-sin120×sin40].....
cos40×[cos^2 120.cos^2 40 - sin^2 120.sin^2 40]....
cos40× [1/4.cos^2 40 - 3/4.sin^2 40]....
(cos40)/4 × [cos^2 40 - 3sin^2 40]....
(cos40)/4 × [(1-sin^2 40) - 3sin^2 40]...
(cos40)/4 × [1-4sin^2 40]....
cos40[1/4 - sin^2 40]....
(cos40)[1/4 - 1 + cos^2 40]....
[(cos40) - (3cos^3 40)]/4....
[cos3(40)]/4....
[cos120]/4....
[-1/2]/4....
[-1/8]....
Hence proved....
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