What is the general solution for 3sin(x)=sin(x)-1 ?

The general solution for 3sin(x)=sin(x)-1 is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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3sin(x)=sin(x)-1

3 sin (x) = sin (x) - 1

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Solution steps

3 sin (x) = sin (x) - 1

Solve by substitution

sin (x) = - \frac{1}{2}

sin (x) = - \frac{1}{2} : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Combine all the solutions

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

1 - tan (- x) = sec (- x)

cos (2 x - a) = sin (3 x)

x, 2 cos (x) = 3

41 sin^{2} (x) + 32 sin (x) - 9 = 0

cos (x - 3 0^{\circ}) = 2 sin (x)

What is the general solution for 3sin(x)=sin(x)-1 ?
The general solution for 3sin(x)=sin(x)-1 is x=(7pi)/6+2pin,x=(11pi)/6+2pin