## Butterfly16 2 years ago 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

1. NotTim

i guess change the left side?

2. Butterfly16

Can you show me how? I don't understand how to apply the identities.

3. mathdude69

are those 2's all ² ?

4. Butterfly16

Ops, yeah.

5. mathdude69

No prob. If you hold down the ALT key and press 0179 on the number pad, you can get ². 0179 gives you ³ as well. as for this problem, can you rewrite sec²x a different way? What is it defined as? Once you do that you should see that something cancels out.

6. Butterfly16

Is it 1+tan^2x ? I couldnt get the thing to work, I dont have a number pad on my computer :(

7. mathdude69

Yep, and that's an identity as well. http://en.wikipedia.org/wiki/Pythagorean_trigonometric_identity#Related_identities

8. Butterfly16

I'm still confused :/

9. mathdude69

You're done with the problem! :) The left side is 1 + tan^2x right? There's an identity that says sec^2 x = 1 + tan^2 x , which is what we have here.

10. Butterfly16

What would cancel out?

11. Butterfly16

What about the 1+ in the front and the sin^2x?

12. mathdude69

Did you change sec ^2 x to 1 / cos^2x on the left hand side? sorry, there isn't a cancellation, but it will turn into another function.

13. Butterfly16

I'm still confused, do you mind typing out the steps? I'm still not understanding how to get the answer :(

14. mathdude69

Sure, but I'm going to have you do some work inbetween :) Step 1: With these identity problems our first step will always be to break apart trig functions into their definitions. So for this equation we have: $1 + \sec ^{2}x \sin^{2}x = \sec^{2}x$ In order for this to be an identity we need to get the Left hand side equal to the right hand side. If we change the sec²x on the left hand side into $\frac{ 1 }{ \cos^{2}x }$, what does the left hand side then simplify into?

15. Butterfly16

Hmmm, would it be$1+\frac{ 1 }{ \cos^2x }\sin^2x$ ?

16. Butterfly16

@exitfreshly Do you know to solve this?

17. exitfreshly

My brain hurts too much to try and do trig substitutions right now. Try backsolving what you think might be the answer, maybe; besides that I can't unfortunately be of much help.