What is the general solution for tan(2x)sin(x)=sin(x) ?

The general solution for tan(2x)sin(x)=sin(x) is x=2pin,x=pi+2pin,x= pi/8+(pin)/2

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tan(2x)sin(x)=sin(x)

tan (2 x) sin (x) = sin (x)

x = 2 πn, x = π + 2 πn, x = \frac{π}{8} + \frac{πn}{2}

Solution steps

tan (2 x) sin (x) = sin (x)

Subtract

sin (x)

from both sides

tan (2 x) sin (x) - sin (x) = 0

Factor

tan (2 x) sin (x) - sin (x) : sin (x) (tan (2 x) - 1)

sin (x) (tan (2 x) - 1) = 0

Solving each part separately

sin (x) = 0 or tan (2 x) - 1 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

tan (2 x) - 1 = 0 : x = \frac{π}{8} + \frac{πn}{2}

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{π}{8} + \frac{πn}{2}

sin (u) = - \frac{3}{5}, \frac{3 π}{2} < u < 2 π

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

sin (x) + cos (x) = 2

3 cos (B) - 1 = 5 cos (B) + 1

cos (θ) = \frac{3}{4}

What is the general solution for tan(2x)sin(x)=sin(x) ?
The general solution for tan(2x)sin(x)=sin(x) is x=2pin,x=pi+2pin,x= pi/8+(pin)/2