I assume you mean:
Could someone please help me with this? I can't figure out what properties to use.
Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation.
1 + sec2x sin2x = sec2x
Hey, no problem, just wanted to make sure, and just use the caret symbol "^" to denote exponentiation.
You should be familiar with a Pythagorean identity involving the secant function. That along with rewriting (can you think of a simpler way to write this term?) should help quite a bit.
You want the form involving the square of the secant function, and since the right side of the Pythagorean identity you cited is 1, you should divide through by , or equivalently, multiply through by . In fact, if you do the latter, you get the very equation you are given to verify!
I only wanted you to use the definition of the secant function for the first term on the left to get 1, as you did, but for the other terms, just use the square of the secant function, and you will find you will get the equation you are trying to verify.