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Butterfly16
 3 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
Butterfly16
 3 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

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NotTim
 3 years ago
Best ResponseYou've already chosen the best response.0i guess change the left side?

Butterfly16
 3 years ago
Best ResponseYou've already chosen the best response.0Can you show me how? I don't understand how to apply the identities.

mathdude69
 3 years ago
Best ResponseYou've already chosen the best response.0are those 2's all ² ?

mathdude69
 3 years ago
Best ResponseYou've already chosen the best response.0No 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.

Butterfly16
 3 years ago
Best ResponseYou've already chosen the best response.0Is it 1+tan^2x ? I couldnt get the thing to work, I dont have a number pad on my computer :(

mathdude69
 3 years ago
Best ResponseYou've already chosen the best response.0Yep, and that's an identity as well. http://en.wikipedia.org/wiki/Pythagorean_trigonometric_identity#Related_identities

Butterfly16
 3 years ago
Best ResponseYou've already chosen the best response.0I'm still confused :/

mathdude69
 3 years ago
Best ResponseYou've already chosen the best response.0You'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.

Butterfly16
 3 years ago
Best ResponseYou've already chosen the best response.0What would cancel out?

Butterfly16
 3 years ago
Best ResponseYou've already chosen the best response.0What about the 1+ in the front and the sin^2x?

mathdude69
 3 years ago
Best ResponseYou've already chosen the best response.0Did 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.

Butterfly16
 3 years ago
Best ResponseYou've already chosen the best response.0I'm still confused, do you mind typing out the steps? I'm still not understanding how to get the answer :(

mathdude69
 3 years ago
Best ResponseYou've already chosen the best response.0Sure, 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?

Butterfly16
 3 years ago
Best ResponseYou've already chosen the best response.0Hmmm, would it be\[1+\frac{ 1 }{ \cos^2x }\sin^2x\] ?

Butterfly16
 3 years ago
Best ResponseYou've already chosen the best response.0@exitfreshly Do you know to solve this?

exitfreshly
 3 years ago
Best ResponseYou've already chosen the best response.0My 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.
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