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Math Help - Identities

  1. #1
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    Identities

    Complete the identity:

    tan^2x - 3sinx tan x sec x

    a) -2tan^2x
    b) 1+cotx
    c) sinx cscx
    d) secx cscx
    Last edited by mr fantastic; March 17th 2010 at 04:08 AM. Reason: Changed post title
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by kenzie103109 View Post
    Complete the identity:

    tan^2x - 3sinx tan x sec x

    a) -2tan^2x
    b) 1+cotx
    c) sinx cscx
    d) secx cscx
    Hi kenzie103109,

    \tan^2 x-3 \sin x \tan x \sec x=

    \tan^2 x - \tan x\left(3 \sin x \frac{1}{\cos x}\right)=

    \tan^2x - \tan x\left(3 \: \frac{\sin x}{\cos x}\right)=

    \tan^2x - \tan x(3 \tan x)=

    \tan^2 x-3 \tan^2x=

    -2 \tan^2 x
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  3. #3
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    Well

    I understand the question to be:
    tan^2(x) -3\times sin(x)\times tan(x)\times sec(x)
    If I understood it correctly that is equal to:


    tan^2(x)-3\times sin(x)\times \frac{sin(x)}{cos(x)} \times \frac{1}{cos(x)}
    tan^2(x)-3\times \frac{sin^2(x)}{cos^2(x)}

    equals:
    tan^2(x)-3tan^2(x) = -2tan^2(x)
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