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

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

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sin(x)+sqrt(2)=-sin(x)

sin (x) + 2 = - sin (x)

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

Solution steps

sin (x) + 2 = - sin (x)

Solve by substitution

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

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

Combine all the solutions

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

cos (x) = \frac{12}{13}

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

cos (y) = 0

2 sin^{2} (x) - 3 sin (x) = - 1

3 cos^{2} (θ) + 2 sin (θ) - 1 = 0

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