What are the steps to prove the Trigonometry identity?

Question

sec(x).cosec(x)+sin(x).sec(x)=cosec(x).sec(x)

Answer 1

Given Sec(x)Cosec(x)+Sin(x)Sec(x) = Cosec(x)Sec(x)

Now i assume it to Sec(x)Cosec(x)+Sin(x)Sec(x) = Cosec(x)Sec(x)Cos^2x

Lefthandside identity = Sec(x)Cosec(x)+Sin(x)Sec(x)

Common out Sec(x).

= Sec(x)(Cosecx+Sinx)

= Sec(x)(1/Sinx+Sinx)

= Sec(x)(1+Sin^2x)/Sinx

= Sec(x)(cos^2x)/Sin(x)

= Sec(x)Cosec(x)(cos^2x)

= riight hand side identity