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

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

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

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

x = πn, x = \frac{π}{2} + πn

Solution steps

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

Subtract

sin (x) cos (x)

from both sides

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

Rewrite using trig identities

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

Multiply both sides by

2

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

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

(2 sin (2 x) - 1) (3 tan (2 x) - 1) = 0

- 0.2588 + 0.9659 tan (b) = 1.4201

2 cot^{2} (t) sin (t) - cot^{2} (t) = 0

7 cos (x) = - 1

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