What is the general solution for sqrt(2)sin^2(θ)-cos(θ)=0 ?

The general solution for sqrt(2)sin^2(θ)-cos(θ)=0 is θ= pi/4+2pin,θ=(7pi)/4+2pin

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sqrt(2)sin^2(θ)-cos(θ)=0

2 sin^{2} (θ) - cos (θ) = 0

θ = \frac{π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn

Solution steps

2 sin^{2} (θ) - cos (θ) = 0

Rewrite using trig identities

- cos (θ) + (1 - cos^{2} (θ)) 2 = 0

Solve by substitution

cos (θ) = - 2, cos (θ) = \frac{2}{2}

cos (θ) = - 2 :

No Solution

cos (θ) = \frac{2}{2} : θ = \frac{π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn

Combine all the solutions

θ = \frac{π}{4} + 2 πn, θ = \frac{7 π}{4} + 2 πn

csc (θ) = \frac{2}{3}

cos (\frac{x}{2}) (\frac{1}{2}) = 0

cos (x) = 0.83

sin (x + \frac{π}{4}) = \frac{1}{2}, 0 \leq x \leq 2 π

cos (2 x) + 7 cos (x) + 4 = 0

What is the general solution for sqrt(2)sin^2(θ)-cos(θ)=0 ?
The general solution for sqrt(2)sin^2(θ)-cos(θ)=0 is θ= pi/4+2pin,θ=(7pi)/4+2pin