What is the general solution for sqrt(2)sin(x)+1=cos(2x) ?

The general solution for sqrt(2)sin(x)+1=cos(2x) is x=2pin,x=pi+2pin,x=(5pi)/4+2pin,x=(7pi)/4+2pin

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sqrt(2)sin(x)+1=cos(2x)

2 sin (x) + 1 = cos (2 x)

x = 2 πn, x = π + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Solution steps

2 sin (x) + 1 = cos (2 x)

Subtract

cos (2 x)

from both sides

2 sin (x) + 1 - cos (2 x) = 0

Rewrite using trig identities

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

Solve by substitution

sin (x) = 0, sin (x) = - \frac{2}{2}

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = - \frac{2}{2} : x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

sin (2 x) = - 1 sin (x)

cos (x) = \frac{1}{6}

2 cos^{2} (θ) + 9 cos (θ) + 4 = 0

3 sin^{2} (x) - 5 sin (x) - 2 = 0

csc (x) = - \frac{2}{3}

What is the general solution for sqrt(2)sin(x)+1=cos(2x) ?
The general solution for sqrt(2)sin(x)+1=cos(2x) is x=2pin,x=pi+2pin,x=(5pi)/4+2pin,x=(7pi)/4+2pin