Simplify trig identities

Question

1+cosx  =   sinx

 sinx          1-cosx

Answer 1

Can be proven by Cross Multiplication

 

 1 + CosX   =  Sin X      

   Sin X           1 - CosX

 

 ( 1 +CosX ) ( 1 - Cos X)  = Sin² X

 

    1  - Cos ² X  = Sin ²X

 

       Sin ² X  = Sin ² X

 

   Otherwise right hand side has to be multiplied by ( 1-cosX ) / ( 1 -cosX )

Answer 2

(1+cos(x))/sin(x) =? sin(x)/(1-cos(x))

(1+cos(x))(1-cos(x))/( (sin(x)) (1-cos(x)) ) =? sin(x)/(1-cos(x))

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

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

sin(x)/(1-cos(x)) = sin(x)/(1-cos(x)) √