how to verify this identity

Question

(cscx/1+cscx)=1-sinx/Cos^2x

Answer 1

csc(x)/1+cscx = 1-sinx/cos^2x

We know that cscx = 1/sinx and sin^2x+cos^2x = 1

Left hand side

= cscx/1+cscx

= (1/sinx)/1+(1/sinx)

= (1/sinx)/(sinx+1/sinx)

= 1/sinx+1

multiple by 1-sinx

= (1/1+sinx)(1-sinx/1-sinx)

= 1-sinx/1-sin^2x

= 1-sinx/cos^2x

= Right hand side