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=(3pi)/4+2pin,x=(5pi)/4+2pin

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

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

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

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

cos (x) = 2 :

No Solution

Combine all the solutions

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

sec (3 x) = \frac{2}{3}, 0 \leq x \leq 2 π

sec (4 x) - 2 = 0

2 cos (θ) sin (θ) = cos (θ)

- 2 sin (x) = 0

sin (3 x) = \frac{3}{2}

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=(3pi)/4+2pin,x=(5pi)/4+2pin