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

The general solution for sin^2(x)=sin(2x) is x=2pin,x=pi+2pin,x=1.10714…+pin

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sin^2(x)=sin(2x)

sin^{2} (x) = sin (2 x)

x = 2 πn, x = π + 2 πn, x = 1.10714 \dots + πn

Solution steps

sin^{2} (x) = sin (2 x)

Subtract

sin (2 x)

from both sides

sin^{2} (x) - sin (2 x) = 0

Rewrite using trig identities

sin^{2} (x) - 2 cos (x) sin (x) = 0

Factor

sin^{2} (x) - 2 cos (x) sin (x) : sin (x) (sin (x) - 2 cos (x))

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

Solving each part separately

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) - 2 cos (x) = 0 : x = arctan (2) + πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = arctan (2) + πn

Show solutions in decimal form

x = 2 πn, x = π + 2 πn, x = 1.10714 \dots + πn

sin (5 x + 50) = cos (4 x - 23)

tan (x) = 1.2

tan (x) = 0.9

x, sin (x) + cos (x) = 0

6 sin (x) = 3

What is the general solution for sin^2(x)=sin(2x) ?
The general solution for sin^2(x)=sin(2x) is x=2pin,x=pi+2pin,x=1.10714…+pin