prove that (1+cosx/sinx)+(sinx/1+cosx) = 2cscx

Question

proving only , no simplifying

Answer 1

Left hand side identity = (1+cosx/sinx)+(sinx/1+cosx)

= [(1+cosx)^2+sn^2x]/sinx(1+cosx)

= [1+cos^2x+2cosx+sin^2x]/sinx(1+cosx)

= [1+1+2cosx]/sinx(1+cosx)

= (2+2cosx)/sinx(1+cosx)

= 2(1+cosx)/sinx(1+cosx)

= 2/sinx

= 2cscx

= right hand side identity.