Prove the Indentity

Question

prove secx+1/tanx=sinx/1-cosx.

 

Answer 1

Left hand side identity =

= (Secx+1)/Tanx

= [(1/Cosx)+1]/Tanx

= [(1+Cosx)/Cosx]/(Sinx/Cosx)

= (1+Cosx)/Sinx

Multple to numarator and denominator by (1-Cosx).

= (1+Cosx)(1-Cosx)/Sinx(1-Cosx)

= (1-Cos^2x)/Sinx(1-Cosx)

= Sin^2x/Sinx(1-Cosx)

= Sinx/(1-Cosx)

= Right hand side identity.