Math, asked by Anonymous, 1 year ago

Evaluate- cos40°cos100°cos160°

Answers

Answered by Anudeepkalyadapu11
12
Hey, here is your answer....

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....

hope this helps you....

plzz mark it as brainliest....

IncredibleManiac: It is cos 100 not cos 80
Answered by anushkasharma8840
7

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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