What is the general solution for sin^2(x)-tan(x)=0 ?

The general solution for sin^2(x)-tan(x)=0 is x=2pin,x=pi+2pin

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

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

x = 2 πn, x = π + 2 πn

Solution steps

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

Express with sin, cos

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

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

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

Factor

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

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

Solving each part separately

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

- 1 + sin (x) cos (x) = 0 :

No Solution

Combine all the solutions

x = 2 πn, x = π + 2 πn

6 sin^{3} (x) + 7 sin^{2} (x) - sin (x) - 2 = 0

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

tan (x) = \frac{1}{sec ( x )}

2 \cdot cos (2 x) - 1 = 0

sin^{2} (x) = \frac{( 7 m - 2 )}{8}

What is the general solution for sin^2(x)-tan(x)=0 ?
The general solution for sin^2(x)-tan(x)=0 is x=2pin,x=pi+2pin