simplifying trig identities in terms of single trigonometric function or constant

Question

How do you simplify 1/sec² x + 1/csc²x

Answer 1

First of all, it's helpful to get everything in terms of sines and cosines. The reciprocal trig identities say that 1/sec²x = cos²x and 1/csc²x = sin²x

After that you have: cos²x + sin²x. Using the pythagorean identity, that simplifies to 1.

So to sum up:

1. Use Reciprocal identiites:
2. 1/sec²x = cos²x
3. 1/csc²x = sin²x
4. Use Pythagorean identity:
5. cos²x + sin²x = 1