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Math Help - Verifing Idnetities Help

  1. #1
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    Verifing Idnetities Help

    I'm currently trying to verify these three identities and they are giving me some trouble.
    They are:
    1.(sin^2x-2sin^4x+sin^6x)=sin^2xcos^4x
    2. secx+cscx/1+tanx=cscx
    3. cosx-(cosx/1-tanx)=sinxcosx/sinx-cosx

    Thanks in advance
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  2. #2
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    Quote Originally Posted by Ciccone07 View Post
    I'm currently trying to verify these three identities and they are giving me some trouble.
    They are:
    1.(sin^2x-2sin^4x+sin^6x)=sin^2xcos^4x

    \sin^2x-2\sin^4x+\sin^6x=\sin^2x(1-2\sin^2x+\sin^4x)=\sin^2x(1-\sin^2x)^2=\sin^2x\cos^4x , using \cos^2x+\sin^2x=1 .

    Now you play as above with the other identities...

    Tonio


    2. secx+cscx/1+tanx=cscx
    3. cosx-(cosx/1-tanx)=sinxcosx/sinx-cosx

    Thanks in advance
    .
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  3. #3
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    Tallahassee Florida
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    Trig Identies

    Quote Originally Posted by Ciccone07 View Post
    I'm currently trying to verify these three identities and they are giving me some trouble.
    They are:
    1.(sin^2x-2sin^4x+sin^6x)=sin^2xcos^4x
    2. secx+cscx/1+tanx=cscx
    3. cosx-(cosx/1-tanx)=sinxcosx/sinx-cosx
    Thanks in advance
    I'm currently trying to verify these three identities and they are giving me some trouble.
    They are:
    1.(sin^2x-2sin^4x+sin^6x)=sin^2xcos^4x

    (sin(x))^2 (cos(x))^4
    = (sin(x))^2 ( 1 - sin(x))^2 )^2
    = (sin(x))^2 ( 1 - 2 (sin(x))^2 + (sin(x))^4 )
    = (sin(x))^2 - 2 (sin(x))^4 + (sin(x))^6


    2. secx+cscx/1+tanx=cscx

    (sec(x) + csc(x)) / ( 1 + tan(x))
    = (1/cos(x) + (1/sin(x) ) / (1 + sin(x)/(cos(x) )
    = (1 + cos(x)/sin(x) )/(cos(x) + sin(x) )
    = (1/sin(x) ) ( sin(x) + cos(x) )/(cos(x) + sin(x))
    = 1/sin(x)
    = csc(x)


    3. cosx-(cosx/1-tanx)=sinxcosx/sinx-cosx

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

    = cos(x) sin(x) / (sin(x) - cos(x))


    Kermit
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