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

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

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sqrt(2)sin^2(x)-cos(x)=0

2 sin^{2} (x) - cos (x) = 0

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

Solution steps

2 sin^{2} (x) - cos (x) = 0

Rewrite using trig identities

- cos (x) + (1 - cos^{2} (x)) 2 = 0

Solve by substitution

cos (x) = - 2, cos (x) = \frac{2}{2}

cos (x) = - 2 :

No Solution

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

Combine all the solutions

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

sin^{4} (x) - cos^{4} (x) = 0

tan (θ) cos (θ) + cos (θ) = 0

sin (x) = cos (x), 0 \leq x \leq 2 π

3 cos (θ) = 0

2 sin^{2} (θ) + sin (θ) - 9 = 2 sin (θ) - 8

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