Question

How do I verify that the following equations is an identity: 1+ sec x sin x tan x = sec^2 x

Answer 1

First change sec x sin x tan x to (sinx/cosx)*tanx
= tan^2 x
So you have
1 + tan^2 x = sec^2 x
You can write the left side as
(cos^2 x + sin^2 x)/cos^2 x = 1/cos^2 x = sec^2 x

That completes the proof

Answer 2

Thank you!