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

Question

Prove the identity?

Answer 1

sin²(x)+cos²(x)=1, divide through by cos²(x):

tan²(x)+1=sec²(x);

sec²(x)/csc²(x)=(1/cos²(x))/(1/sin²(x))=

sin²(x)/cos²(x)=(sin(x)/cos(x))²=tan²(x); therefore:

(tan²(x)+1)/csc²(x)=(1+tan²(x))/csc²(x)=tan²(x) QED