Prove the identity: csc x - cot x = sinx/1+cosx

The identity csc x - cot x = sin x/(1+cos x) has to be
proved.

Start from the left hand
side

csc x - cot x

csc x = 1/
sin x and cot x = cos x/ sin x

=> 1/sin x - cos
x/sin x

=> (1 - cos x)/sin
x

=> (1 - cos x)(1 + cos x)/(sin x)*(1 + cos
)

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

=> (sin x)^2/(sin x)*(1 + cos
)

=> sin x / (1 + cos
)

which is the right  hand
side.

This proves csc x - cot x = sin
x/(1+cos x)