Question

cos40° cos 100° cos160° =1/8​

Answer 1

╔═❤️══════════════╗

...HERE GØΣS UR ANS...

╚══════════════❤️═╝

$\huge\mathfrak\orange{bonjour}$

AS THE QUESTION IS TO PROVE

HERES YOUR PROOF

❣

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 IT HELPS U ❣❣

 ❣❣PLEASE MARK MY ANSWER AS BRAINLIEST ❣❣

FOLLOW ME

 ❣❣THANKS ❣❣

☺☺☺

#BEBRAINLY

$\huge\mathfrak{Follow \ Me}$

Answer 2

Answer:

Step-by-step explanation:

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....