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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
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

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NotTimBest ResponseYou've already chosen the best response.0
i guess change the left side?
 one year ago

Butterfly16Best ResponseYou've already chosen the best response.0
Can you show me how? I don't understand how to apply the identities.
 one year ago

mathdude69Best ResponseYou've already chosen the best response.0
are those 2's all ² ?
 one year ago

mathdude69Best ResponseYou've already chosen the best response.0
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.
 one year ago

Butterfly16Best ResponseYou've already chosen the best response.0
Is it 1+tan^2x ? I couldnt get the thing to work, I dont have a number pad on my computer :(
 one year ago

mathdude69Best ResponseYou've already chosen the best response.0
Yep, and that's an identity as well. http://en.wikipedia.org/wiki/Pythagorean_trigonometric_identity#Related_identities
 one year ago

Butterfly16Best ResponseYou've already chosen the best response.0
I'm still confused :/
 one year ago

mathdude69Best ResponseYou've already chosen the best response.0
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.
 one year ago

Butterfly16Best ResponseYou've already chosen the best response.0
What would cancel out?
 one year ago

Butterfly16Best ResponseYou've already chosen the best response.0
What about the 1+ in the front and the sin^2x?
 one year ago

mathdude69Best ResponseYou've already chosen the best response.0
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.
 one year ago

Butterfly16Best ResponseYou've already chosen the best response.0
I'm still confused, do you mind typing out the steps? I'm still not understanding how to get the answer :(
 one year ago

mathdude69Best ResponseYou've already chosen the best response.0
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?
 one year ago

Butterfly16Best ResponseYou've already chosen the best response.0
Hmmm, would it be\[1+\frac{ 1 }{ \cos^2x }\sin^2x\] ?
 one year ago

Butterfly16Best ResponseYou've already chosen the best response.0
@exitfreshly Do you know to solve this?
 one year ago

exitfreshlyBest ResponseYou've already chosen the best response.0
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.
 one year ago
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