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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

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  1. NotTim
    • 3 years ago
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    i guess change the left side?

  2. Butterfly16
    • 3 years ago
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    Can you show me how? I don't understand how to apply the identities.

  3. mathdude69
    • 3 years ago
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    are those 2's all ² ?

  4. Butterfly16
    • 3 years ago
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    Ops, yeah.

  5. mathdude69
    • 3 years ago
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    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
    • 3 years ago
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    Is it 1+tan^2x ? I couldnt get the thing to work, I dont have a number pad on my computer :(

  7. mathdude69
    • 3 years ago
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    Yep, and that's an identity as well. http://en.wikipedia.org/wiki/Pythagorean_trigonometric_identity#Related_identities

  8. Butterfly16
    • 3 years ago
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    I'm still confused :/

  9. mathdude69
    • 3 years ago
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    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
    • 3 years ago
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    What would cancel out?

  11. Butterfly16
    • 3 years ago
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    What about the 1+ in the front and the sin^2x?

  12. mathdude69
    • 3 years ago
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    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
    • 3 years ago
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    I'm still confused, do you mind typing out the steps? I'm still not understanding how to get the answer :(

  14. mathdude69
    • 3 years ago
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    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
    • 3 years ago
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    Hmmm, would it be\[1+\frac{ 1 }{ \cos^2x }\sin^2x\] ?

  16. Butterfly16
    • 3 years ago
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    @exitfreshly Do you know to solve this?

  17. exitfreshly
    • 3 years ago
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    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.

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