How can I solve the trigonometric identity tanA+cotA=2cosec2A?

Question

For starters, I’m not sure which side should be simplified. RHS could have the double angle formula applied while the LHS has more terms. I’ve tried working through multiple ways and all seem to give answers that aren’t even close. I’ve struggled a fair bit with trig identities so any general pointers as well as this question would be greatly appreciated :)

Answer 1

In verifying a trigonometry identity you may choose eather side to transform into the other side.

Usually pick the one that simplifies to a general form.

tan a + cot a

( sin a / cos a) + (cos a / sin a)

Now combine using LCD

Then look at double angle formulas.