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How many solution of the equation please answer me thanks

How many solution of the equation please answer me thanks

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Grade:11

1 Answers

Khimraj
3007 Points
6 years ago
cosθcos2θcos3θ = ¼
2*(2cosθcos3θ)*cos2θ = 1
2*(cos4θ + cos2θ)*cos2θ = 1
2cos4θcos2θ + 2cos22θ  =1
2cos4θcos2θ + cos4θ = 0
cos4θ(2cos2θ +1) = 0
cos4θ = 0  or cos2θ = -1/2
4θ = (2k+1)π/2   or 2θ = 2kπ ± 2π/3
θ =  (2k+1)π/8    or θ = kπ ± π/3
So θ = { π/8, π/3, 3π/8, 5π/8, 2π/3, 7π/8 }.
So no of solution between 0 and  π is 6.
Hope it clears. If you like answer then please approve it.

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