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Question

If 3sin θ=cos θ, find the value of  3 cos2θ+2 cos θ3 cos θ+2


Solution

Given ,3 sin θ=cos θ             

    sinθcosθ=13 or tan θ=13


    tan θ=tan 30θ=30

Simplifying the given equation, we get

3 cos2θ+2 cos θ3 cos θ+2=cos θ(3 cos θ+2)(3 cos θ+2)

=cos θ
Substituting θ=30, we get

cos 30=32 
 

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