(ii) cos 40° cos 80° cos 160° =-1/8
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Answer:
Step-by-step explanation:
cos 40° cos 80° cos 160°
= (2*cos40.cos80).cos160 /2
But 2cosA.cosB=cos(A+B) + cos(A-B)
= (cos(80+40)+cos(80-40))*cos(180-20)/2
But Cos(180-A) = -CosA
= (cos120 + cos40 ) * (-cos20 )/2
= (-1/2 + cos2(20)) *(-cos20)/2
but Cos2A=2cos²A-1
= (2cos²20-1-1/2) * (-cos20)/2
= (2cos²20-3/2) * (-cos20)/2
= [4cos²20 - 3/2] * (-cos20)/2
= (- 4cos³20 + 3cos20) /4
= (-1/4) [ 4cos³20 - 3cos20]
= (-/14) * (cos3*20)
= (-/14) * (cos60)
= (-/14) (1/2)
= - 1/8.
= R.H.S
Hence Proved
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