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

The general solution for tan(x)=2sin^2(x) is x=2pin,x=pi+2pin,x= pi/4+pin

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

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

x = 2 πn, x = π + 2 πn, x = \frac{π}{4} + πn

Solution steps

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

Subtract

2 sin^{2} (x)

from both sides

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

Express with sin, cos

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

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

Factor

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

sin (x) (1 - 2 sin (x) cos (x)) = 0

Solving each part separately

sin (x) = 0 or 1 - 2 sin (x) cos (x) = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

1 - 2 sin (x) cos (x) = 0 : x = \frac{π}{4} + πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{π}{4} + πn

0 = 4 sin (2 x)

\frac{sin ( 112. 8 ^{\circ} )}{16.1} = \frac{sin ( x )}{12.2}

(sin (x) + cos (x))^{2} = \frac{3}{2}

2 sin^{2} (t) - sin (t) - 1 = 0

cos (x) = - \frac{1}{5 2}

What is the general solution for tan(x)=2sin^2(x) ?
The general solution for tan(x)=2sin^2(x) is x=2pin,x=pi+2pin,x= pi/4+pin