What is the general solution for ((1-(cos(x))^2))/((1+sin(x)))=sin(x) ?

The general solution for ((1-(cos(x))^2))/((1+sin(x)))=sin(x) is x=2pin,x=pi+2pin

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((1-(cos(x))^2))/((1+sin(x)))=sin(x)

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

x = 2 πn, x = π + 2 πn

Solution steps

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

Subtract

sin (x)

from both sides

\frac{1 - cos ^{2} ( x )}{1 + sin ( x )} - sin (x) = 0

Simplify

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

\frac{1 - cos ^{2} ( x ) - sin ( x ) ( 1 + sin ( x ) )}{1 + sin ( x )} = 0

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

1 - cos^{2} (x) - sin (x) (1 + sin (x)) = 0

Rewrite using trig identities

- sin (x) = 0

Divide both sides by

- 1

sin (x) = 0

General solutions for

sin (x) = 0

x = 0 + 2 πn, x = π + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 2 πn, x = π + 2 πn

x, arctan (x) = 0

5 sin (x) = - 3

csc^{2} (x) = 2 \cdot cot^{2} (x)

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

3 \cdot 2 = \frac{50 sin ( x )}{9.8}

What is the general solution for ((1-(cos(x))^2))/((1+sin(x)))=sin(x) ?
The general solution for ((1-(cos(x))^2))/((1+sin(x)))=sin(x) is x=2pin,x=pi+2pin