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math

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i have a few questions

cosx + cosx =2secx
----- -----
1+sinx 1-sinx


cos(x-B)-cos(x-B) = 2sinxsinB


csc2x= 1 secx cscx
---
2


cotx= cos5x+cos3x
-----------
sin 5x-sin 3x

  • math -

    for the first one:

    LS = cosx/(1+sinx) + cosx/(1-sinx)

    getting a common denominator of (1+sinx)(1-sinx)
    = [cosx(1-sinx) + cosx(1+sinx)]/(1+sinx)(1-sinx)
    = 2cosx/(1-sin^2)
    = 2cosx/cos^2x
    = 2/cosx
    = 2secx
    = RS

    for cos(x-B)-cos(x-B) = 2sinxsinB

    use the formula cos(A-B) = cosAcosB + sinAsinB on the Left Side, it comes apart very nicely after that

    For the last two, try changing all trig ratios into sines and cosines.
    Show me what you get

  • math -

    i don't understand how to use the formula in the second problem. what would i plug into A and B?

  • math -

    cos(x-B)-cos(x+B) = 2sinxsinB

    LS
    = cosxcosB + sinxsinB - (cosxcosB - sinxsinB)
    =2sinxsinB
    = RS

  • math -

    for cos(x-B)-cos(x-B) = 2sinxsinB
    you must have a typo, the LS is zero the way it stands
    I am sure you meant

    cos(x-B)-cos(x+B) = 2sinxsinB

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