What is the general solution for 3sin(x)+sqrt(2)=sin(x) ?

The general solution for 3sin(x)+sqrt(2)=sin(x) is x=(5pi)/4+2pin,x=(7pi)/4+2pin

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3sin(x)+sqrt(2)=sin(x)

3 sin (x) + 2 = sin (x)

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

Solution steps

3 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

sin (x) cos (x) - sin (x) = 0

tan^{2} (x) = 2 tan (x) sin (x)

tan^{2} (x) - 3 tan (x) = 0

sin (u) = - \frac{3}{5}

2 sin^{2} (x) = cos (x) + 1

What is the general solution for 3sin(x)+sqrt(2)=sin(x) ?
The general solution for 3sin(x)+sqrt(2)=sin(x) is x=(5pi)/4+2pin,x=(7pi)/4+2pin