## Butterfly16 Group Title 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 one year ago one year ago

1. NotTim Group Title

i guess change the left side?

2. Butterfly16 Group Title

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

3. mathdude69 Group Title

are those 2's all ² ?

4. Butterfly16 Group Title

Ops, yeah.

5. mathdude69 Group Title

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 Group Title

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

7. mathdude69 Group Title

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

8. Butterfly16 Group Title

I'm still confused :/

9. mathdude69 Group Title

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 Group Title

What would cancel out?

11. Butterfly16 Group Title

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

12. mathdude69 Group Title

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 Group Title

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

14. mathdude69 Group Title

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 Group Title

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

16. Butterfly16 Group Title

@exitfreshly Do you know to solve this?

17. exitfreshly Group Title

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.