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

The general solution for cos(x)sin(x)=sin(x) is x=2pin,x=pi+2pin

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cos(x)sin(x)=sin(x)

cos (x) sin (x) = sin (x)

x = 2 πn, x = π + 2 πn

Solution steps

cos (x) sin (x) = sin (x)

Subtract

sin (x)

from both sides

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

Factor

cos (x) sin (x) - sin (x) : sin (x) (cos (x) - 1)

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

Solving each part separately

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

cos (x) - 1 = 0 : x = 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn

sec^{2} (x) - 1 = 1

sec (θ) = 8

x, 2 cos (2 x) = 0

tan (2 θ) + tan (2 θ) sin (2 θ) = 0

3 cot (\frac{1}{4} x) = 3

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