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Christians4

  • 2 years ago

Prove: (sinx + cosx) (Tan^2x+1/tanx) = 1/cosx + 1/sinx Picture below for what it looks like properly

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  1. Christians4
    • 2 years ago
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    tell me if you need clarification i can drop LS and RS

  2. Christians4
    • 2 years ago
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    yes your back!

  3. lgbasallote
    • 2 years ago
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    hmm seems i really can't figure out what you mean. maybe it's time to show the picture

  4. Christians4
    • 2 years ago
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    |dw:1352211230059:dw|

  5. Christians4
    • 2 years ago
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    |dw:1352211285143:dw|

  6. lgbasallote
    • 2 years ago
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    ahh

  7. lgbasallote
    • 2 years ago
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    here's a hint that might help: \[\huge \tan^2 x + 1 = \sec^2 x\] and \[\huge \sec^2 x = \frac1{\cos^2 x}\] try solving it

  8. Christians4
    • 2 years ago
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    sec

  9. Christians4
    • 2 years ago
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    I ended up getting (sinx+cosx) (1/cosxsinx) for my left side

  10. Christians4
    • 2 years ago
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    woo it worked

  11. Christians4
    • 2 years ago
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    How do I prove identities that are like this:

  12. Christians4
    • 2 years ago
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    1+tanx/1-tanx = Tan (x+pi/4)

  13. myininaya
    • 2 years ago
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    \[\frac{1+\tan(x)}{1-\tan(x)}=\tan(x+\frac{\pi}{4})\] I would write each side so that the function tan( ) only contains x and not both x & x+pi/4. You the sum identity for tan. If you don't know it write both sides in terms of sine and cosine. Use the sum identities for them to expand tan(x+pi/4)

  14. Christians4
    • 2 years ago
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    sum identity for tan?

  15. Christians4
    • 2 years ago
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    I know the cos and sin ones

  16. Christians4
    • 2 years ago
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    is it just those over eachother?

  17. Christians4
    • 2 years ago
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    oops im confused.

  18. Christians4
    • 2 years ago
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    do u simply mean sinx/cosx?

  19. phi
    • 2 years ago
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    try using tan = sin/cos and see how it works out

  20. Christians4
    • 2 years ago
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    alright but on the R.S what do i do with the (x +pi/4)

  21. myininaya
    • 2 years ago
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    \[\tan(x+\frac{\pi}{4})=\frac{\sin(x+\frac{\pi}{4})}{\cos(x+\frac{\pi}{4})}\] Use sum identity for sine and cosine.

  22. phi
    • 2 years ago
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    remember sin(a+b)= sin(a)cos(b) + cos(a) sin(b) and cos(a+b)= cos(a)cos(b)- sin(a)sin(b)

  23. Christians4
    • 2 years ago
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    I plugged in the sum identity but i dont know what do to next I have sin and cosx's which i dont know what to do with

  24. phi
    • 2 years ago
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    write down what you have so far

  25. Christians4
    • 2 years ago
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    sinxcospi/4 +cpsxsinpi/4 / cospi/4cosx + sinpi/4sinx

  26. phi
    • 2 years ago
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    pi/4 is 45º it is good to have memorized cos(45) and sin(45)

  27. Christians4
    • 2 years ago
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    oh i knew that but can i convert it in the eqqn?

  28. Christians4
    • 2 years ago
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    so i could right 45deg instead of pi/4?

  29. phi
    • 2 years ago
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    btw, notice that you have the wrong sign in the denominator

  30. phi
    • 2 years ago
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    pi/4 and 45 mean the same thing.... it matters when using a calculator, or in certain math operations where radians are more useful... but the cos(45º) = cos(pi/4 radians)

  31. phi
    • 2 years ago
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    just like 1 foot is the same as 12 inches

  32. Christians4
    • 2 years ago
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    alright thanks

  33. Christians4
    • 2 years ago
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    I think i got it, gotta head to class now, ill ask teacher if hes free

  34. Christians4
    • 2 years ago
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    Thanks for your help

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