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CKaterinaR

  • 2 years ago

1 + sec^2 x sin^2 x = sec^2 x Verify this trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation.

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  1. cwrw238
    • 2 years ago
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    LHS: use sec^2 x = 1 /cos^2 x

  2. CKaterinaR
    • 2 years ago
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    Thanks for answering but I still don't get it. What do you mean?

  3. cwrw238
    • 2 years ago
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    LHS = 1 + sin^2 x ------- cos^2 x

  4. cwrw238
    • 2 years ago
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    and sin^2 x ------- = tan^2 x cos^2 x

  5. cwrw238
    • 2 years ago
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    so LHS = 1 + tan^2 x

  6. CKaterinaR
    • 2 years ago
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    ok... so let me see if this will help you help me understand this better. I know that I'm supposed to do something with the left side of the equation to make it sec^2x. correct?

  7. cwrw238
    • 2 years ago
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    right

  8. CKaterinaR
    • 2 years ago
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    I just don't see how the cos^2x in the denomenator fits in. I'm sorry I truly suck at this :(

  9. cwrw238
    • 2 years ago
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    yes these can be tricky - you must have a good knowledge of the trig identities sometimes you just try different ones to see if there are any connections - i was aiming for 1 + tan^2 x because i knew that sec^2 x = 1 + tan^2 x

  10. cwrw238
    • 2 years ago
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    i introduced the cos^2x because sin^2 x/cos^2 x = tan^2 x and sec^2 x = 1/cos^2 x

  11. CKaterinaR
    • 2 years ago
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    OK so how would I put that together to get the answer

  12. cwrw238
    • 2 years ago
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    if you google trigonometrical identities you'll a list of them

  13. CKaterinaR
    • 2 years ago
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    starting from the original equation how do I use what you gave me.

  14. cwrw238
    • 2 years ago
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    well we got LHS = 1 + tan^2 x and this equals RHS sec^2 x

  15. CKaterinaR
    • 2 years ago
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    yes but then again so does 1+ sec^2x sin^2x. I need to transform (1+sec^2xsin^2x) and make it read sec^2x

  16. cwrw238
    • 2 years ago
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    LHS = 1+sec^2xsin^2x) = 1 + sin^2 x ------ (because sec^2 x = 1 / cos^2 x) cos^2 x = 1 + tan^2x = sec^2 x ( because sec^2x = 1 + tan^2 x is a standard identity) = RHS

  17. CKaterinaR
    • 2 years ago
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    Ohhhhh got it wow! OK. Thank you so much. You see I suck so bad that even when you are plainly explaining it to me I still dont get it. But now I do. Again thank you for helping me :)

  18. cwrw238
    • 2 years ago
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    yw

  19. jishan
    • 2 years ago
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    |dw:1354034596449:dw|

  20. CKaterinaR
    • 2 years ago
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    above the last equal sign.... what does it say? 1/??

  21. CKaterinaR
    • 2 years ago
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    oh wait is it 1/cos^2x ?

  22. jishan
    • 2 years ago
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    yeah sister

  23. CKaterinaR
    • 2 years ago
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    awesome.... ok thanks but why is yours different than the other one? is it wrong or is this just another way to do it

  24. cwrw238
    • 2 years ago
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    no - they are both acceptable - just another way to do it

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