Solve sin2 theta cos theta 1 4 for theta and write the values of theta in the interval 0 l...........

Mathematics (NDA) Trigonometry

Solve sin²θ -cosθ=1/4 for θ and write the values of θ in the interval 0≤θ ≤2π?

Θ=π/3,5π/2

Θ=-π/3,5π/3

Θ=π/3,5π/3

Θ=π/2,5π/3

Eθuation sin²θ -cosθ=1/4

1-cos ²θ - cosθ=1/4

cos ²θ + cosθ -3/4=0

4 cos ²θ +4 cosθ -3 =0

(2cosθ -1)( 2cosθ+3)=0

Cosθ =1/2 .-3/2

Cosθ =-3/2 is not possible as -1 ≤cosθ ≤1

Cosθ =1/2

Cosθ = Cosπ/3

Θ =2nπ±π/3 ,n?I

For the given interval n=0 and n=1

Θ=π/3,5π/3

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