Math, asked by indranihazra8, 9 months ago

cos 40° cos 100° cos 160°
=1/8​

Answers

Answered by sjshah0603
5

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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Answered by Anonymous
1

Answer:

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