Question

PLEASE HELP!!

Answer 1

You're going to have to break all of these identities into sin and cos, and then just resolve them like normal.

Answer 2

Answer:

$\frac{ \tan(x) + \cot(x) }{ \csc(x) \cos(x) } \\ \\ = \frac{ \tan(x) + \cot(x) }{ \cot(x) } \\ \\ = \frac{ { \tan }(x) }{ \cot(x) } + 1$

but cot is an inverse of tan:

$= { \tan }^{2} x + 1$

therefore:

${ \tan }^{2} x + 1 = { \sec }^{2} x$

#proved