1+tan^2X/csc^2x=tan^2x

Question

Prove the identity?

Answer 1

Left hand side identity

= (1+Tan^2x)/Csc^2x

= (1+Tan^2x)/(1/Sin^2x)

= Sin^2x(1+Tan^2x)

= (1-Cos^2x)(1+Tan^2x)

= 1+Tan^2x-Cos^2x-Cos^2xTan^2x

= 1+Tan^2x-Cos^2x-Cos^2x(Sin^2x/Cos^2x)

= 1+Tan^2x-Cos^2x-Sin^2x

= 1+Tan^2x-(Cos^2x+Sin^2x)

= 1+Tan^2x-1

= Tan^2x

= Right hand side identity.