Prove that 1/secx+tanx=secx-tanx

Question

Please help me answer my h.w

Thank you.

Answer 1

Multiply the left hand side by secx - tanx to obtain (secx - tanx) / (sec²x - tan²x)

Now, recall that 1 + tan²x = sec²x. So, sec²x - tan²x = 1.

So, the left hand side simplifies to (secx - tanx) / 1 = secx - tanx = right hand side