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

The general solution for 2sin(2x)=sin^2(x) is x=2pin,x=pi+2pin,x=1.32581…+pin

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

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

x = 2 πn, x = π + 2 πn, x = 1.32581 \dots + πn

Solution steps

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

Subtract

sin^{2} (x)

from both sides

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

Rewrite using trig identities

- sin^{2} (x) + 4 cos (x) sin (x) = 0

Factor

- sin^{2} (x) + 4 cos (x) sin (x) : sin (x) (- sin (x) + 4 cos (x))

sin (x) (- sin (x) + 4 cos (x)) = 0

Solving each part separately

sin (x) = 0 or - sin (x) + 4 cos (x) = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

- sin (x) + 4 cos (x) = 0 : x = arctan (4) + πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = arctan (4) + πn

Show solutions in decimal form

x = 2 πn, x = π + 2 πn, x = 1.32581 \dots + πn

5 sin^{2} (x) = 3 sin (x) + 2

sin^{2} (x) = - (\frac{1}{2})

α, sin^{2} (3 α) = 0.56

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

tan (\frac{π}{2} - x) + 2 tan (\frac{π}{2} + x) = 1

What is the general solution for 2sin(2x)=sin^2(x) ?
The general solution for 2sin(2x)=sin^2(x) is x=2pin,x=pi+2pin,x=1.32581…+pin