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

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

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

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

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

Solution steps

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

Subtract

\frac{tan ( x )}{2}

from both sides

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

Simplify

sin^{2} (x) - \frac{tan ( x )}{2} : \frac{2 sin ^{2} ( x ) - tan ( x )}{2}

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

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

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

98 \cdot sin (θ) - 19.6 \cdot cos (θ) = 75.1

\frac{( sin ( x ) + tan ( x ) )}{1 + cos ( x )} = m \cdot sec (x)

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

\frac{sin ( 2 5 ^{\circ} )}{5} = \frac{sin ( b )}{8}

cos (x) - cos (3 x) = - 2 sin (x)

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