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

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

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sin(x)*cos(x)=sin(2x)

sin (x) \cdot cos (x) = sin (2 x)

x = πn, x = \frac{π}{2} + πn

Solution steps

sin (x) cos (x) = sin (2 x)

Subtract

sin (2 x)

from both sides

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

Rewrite using trig identities

- \frac{sin ( 2 x )}{2} = 0

Multiply both sides by

2

- sin (2 x) = 0

Divide both sides by

- 1

sin (2 x) = 0

General solutions for

sin (2 x) = 0

2 x = 0 + 2 πn, 2 x = π + 2 πn

Solve

2 x = 0 + 2 πn : x = πn

Solve

2 x = π + 2 πn : x = \frac{π}{2} + πn

x = πn, x = \frac{π}{2} + πn

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

sin (θ) = \frac{- 1}{2}, 0 \leq θ \leq 4 π

0 = 2 cos (θ)

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

\frac{cos ( x )}{1 + sin ( x )} = 1 - \frac{sin ( x )}{cos ( x )}

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