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Verify the identity

  1. Feb 21, 2010 #1
    1. The problem statement, all variables and given/known data
    Verify the Identity:

    cos(x)-[cos(x)/1-tan(x)] = [(sin(x)cos(x)]/[sin(x)-cos(x)]

    b]2. Relevant equations[/b]
    reciprocal Identities, quotient Identities, Pythagorean Identities

    3. The attempt at a solution
    cos(x)-[cos(x)/1-tan(x)] = [(sin(x)cos(x)]/[sin(x)-cos(x)]





    and this is where i get stuck cant turn it to [(sin(x)cos(x)]/[sin(x)-cos(x)]
    i hope i wrote the problem right
  2. jcsd
  3. Feb 21, 2010 #2

    Try to multiply [tex]\frac{cos(x)}{cos(x)}[/tex] to the very initial equation on the left-hand side , thus combine the terms into a fraction.
  4. Feb 21, 2010 #3
    when i do that wont i get [-cos^2(x)sin(x)]/[cos(x)-sin(x)]

    then what...sorry I'm not that good as these kinda stuff
  5. Feb 21, 2010 #4
    Now how do you make the denominator of the fraction as sin(x)-cos(x) ?
    [hint: multiply -1]
  6. Feb 21, 2010 #5

    after long starring and thinking a light bulb just lit in my head lol




    [tex]\frac{-\sin(x)\cos(x)}{cos(x)-sin(x)}[/tex] then all multiplied by -1 equals...


    am i right? i hope im right...
  7. Feb 21, 2010 #6

    Yes . You're right!
  8. Feb 21, 2010 #7
    thank you so much for helping me :biggrin:
  9. Feb 21, 2010 #8


    Staff: Mentor

    On a point of terminology, the left-hand side is an expression that is part of an equation, but it's not an equation. It is incorrect to refer to an equation on either side of an equation.
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