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=(3pi)/4+2pin,θ=(5pi)/4+2pin

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sqrt(2)sin^2(θ)+cos(θ)=0

2 sin^{2} (θ) + cos (θ) = 0

θ = \frac{3 π}{4} + 2 πn, θ = \frac{5 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) = - \frac{2}{2}, cos (θ) = 2

cos (θ) = - \frac{2}{2} : θ = \frac{3 π}{4} + 2 πn, θ = \frac{5 π}{4} + 2 πn

cos (θ) = 2 :

No Solution

Combine all the solutions

θ = \frac{3 π}{4} + 2 πn, θ = \frac{5 π}{4} + 2 πn

csc (θ) = - \frac{8}{5}

cos^{2} (x) = 2 cos (x) + 3

3 sin (x) - cos (x) = 3

11 - sin (x) = cos (2 x)

sin^{3} (x) = sin (x), 0 \leq x \leq 2 π

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=(3pi)/4+2pin,θ=(5pi)/4+2pin