Question

cos40 cos 80 cos 160=-1/8 prove it?

Answer 1

Answer:

2*cos40.cos80).cos160 /2

= (cos(80+40)+cos(80-40))*cos(180-20)/2

= (cos120 + cos40 )* (-cos20 )/2 // IU cos(180-A)= -cosA and 2cosA.cosB=cosA+B + cosA-B

=(-1/2 + cos2*20)*(-cos20)/2

=(2cos^2(20)-1-1/2)(-cos20)/2 IU cos2A=2cos^A-1

=(2cos^2(20)-3/2)(-cos20)/2 taking LCM

=-(4cos^3(20)-3cos20)/4 applying reverse identity of cos3A

=-(cos3*20)/4

=-(cos60)/4

=-1/8

hence PROVED...!

Hope it's understandable !!

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