How many solution of the equation please answer me thanks
Chandan Kumar , 6 Years ago
Grade 11
Trigonometry> How many solution of the equation please ...
1 Answers
Khimraj
Last Activity: 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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