The number of solutions of cos(2θ)=sin(θ) in (0,2π) is

Damion Ellis

Damion Ellis

Answered question

2023-02-23

The number of solutions of cos2θ=sinθ in 0,2π is...

Answer & Explanation

Roman Hogan

Roman Hogan

Beginner2023-02-24Added 6 answers

1-2sin2θ=sinθcos2x=cos2x-sin2x&cos2x+sin2x=12sin2θ+sinθ-1=02sin2θ+2sinθ-sinθ-1=02sinθsinθ+1-sinθ+1=0sinθ+12sinθ-1=0
sinθ+1=0 or 2sinθ-1=0
sinθ=-1 or sinθ=12
θ0,2π,θ=π6,5π6,3π2

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