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Question

Find all values of θ between 0o and 180o satisfying the equation : cos6θ+cos4θ+cos2θ+1=0

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Solution

cos6θ+cos4θ+cos2θ+1=0
2cos4θcos2θ+cos4θ+1=0
2cos4θcos2θ+2cos22θ=0
2cos2θ(cos4θ+cos2θ)=0
2cos2θ×2cos3θ×cosθ=0
cosθ=0,cos2θ=0,cos3θ=0
θ=(2n+1)π2 or θ=(2n+1)π4 or θ=(2n+1)

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