I need help in understanding how to identify which identity to use. using this question as an example.

Question

Show that tan theta (sin theta+cot theta cos theata)all over cos theta = sec^2 theta. Please explain.

Answer 1

tan(sin+cot*cos)/cos

When dealing with such a combination of functions, it is usually good to start out by converting everything to sin and cos:

(sin/cos)(sin+(cos/sin)cos)/cos
sin/cos * (sin^2 + cos^2)/sin * 1/cos
(sin^2 + cos^2)/cos^2
1/cos^2
sec^2