What is the general solution for sin(x)tan(x)=sin(x) ?

The general solution for sin(x)tan(x)=sin(x) is x=2pin,x=pi+2pin,x= pi/4+pin

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sin(x)tan(x)=sin(x)

sin (x) tan (x) = sin (x)

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

Solution steps

sin (x) tan (x) = sin (x)

Subtract

sin (x)

from both sides

sin (x) tan (x) - sin (x) = 0

Factor

sin (x) tan (x) - sin (x) : sin (x) (tan (x) - 1)

sin (x) (tan (x) - 1) = 0

Solving each part separately

sin (x) = 0 or tan (x) - 1 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

tan (x) - 1 = 0 : x = \frac{π}{4} + πn

Combine all the solutions

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

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

9 cos^{2} (θ) - 4 = 0

sec (θ) = \frac{2 3}{3}

sin (x + \frac{π}{4}) - sin (x - \frac{5 π}{4}) = \frac{2}{2}

tan (x) = - \frac{4}{3}

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