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If $32 \tan^{8} θ = 2 \cos^{2} α - 3 \cos α$ and $3 \cos 2 θ = 1$ , then the general value of $α$ is

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2nπ,n∈z

nπ±π3;n∈z

2nπ±π3,n∈z

2nπ±2π3,n∈z

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detailed solution

Correct option is D

3cos2θ=1 ⇒tan2θ=1−cos2θ1+cos2θ=12 2cos2α−3cosα=32(116)⇒2cos2α−3cosα−2=0(2cosα+1)(cosα−2)=0⇒cosα=−12=cos2π3General solution is: α=2nπ±2π3;n∈z

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If 32tan8θ=2cos2α−3cosα and 3cos2θ=1 , then the general value of α is

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If $32 \tan^{8} θ = 2 \cos^{2} α - 3 \cos α$ and $3 \cos 2 θ = 1$ , then the general value of $α$ is