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

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

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

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

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

Solution steps

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

Subtract

sin^{2} (x)

from both sides

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

Factor

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

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

Solving each part separately

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

2 cos (x) - sin (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 (θ) - 0.1 cos (θ) = \frac{8.87}{9.8}

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

6 sin^{2} (x) = 5 + cos (x), 18 0^{\circ} \leq x \leq 54 0^{\circ}

\frac{cos ( x )}{2} = \frac{3}{2}

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

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