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Question

cosθ+sinθ=cos2θ+sin2θ Find the value of θ.

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Solution

(cosθcos2θ)(sin2θsinθ)=0
2sin(3θ/2)sin(θ/2)2cos(3θ/2)sin(θ/2)=0
or sin(θ/2){sin(3θ/2)cos(3θ/2)}=0
sin(θ/2)=0 θ/2=nπ or θ=2nπ
sin(3θ/2)cos(3θ/2)=0
tan(3θ/2)=1=tan(π/4)
3θ2=nπ+π4 or θ=2nπ3+π6.

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