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Math Help - [SOLVED] Another Trig Identity Problem...

  1. #1
    Junior Member
    Joined
    Feb 2009
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    [SOLVED] Another Trig Identity Problem...

    I'm having trouble solving this. Can someone please show me?

    tanxsinx
    __________ =
    tanx + sinx


    tanx - sinx
    _________
    tanxsinx

    Thanks!
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  2. #2
    MHF Contributor
    Grandad's Avatar
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    South Coast of England
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    Hello demo1
    Quote Originally Posted by demo1 View Post
    I'm having trouble solving this. Can someone please show me?

    tanxsinx
    __________ =
    tanx + sinx


    tanx - sinx
    _________
    tanxsinx

    Thanks!
    \frac{\tan x\sin x}{\tan x+\sin x}=\frac{\tan x\sin x}{\tan x+\sin x}\times\frac{\cos x}{\cos x}

    =\frac{\sin^2x}{\sin x + \sin x\cos x}

    =\frac{1-\cos^2x}{\sin x(1+\cos x)}

    =\frac{(1-\cos x)(1+\cos x)}{\sin x(1+\cos x)}

    =\frac{1-\cos x}{\sin x}

    =\frac{\tan x}{\tan x}\times\frac{(1-\cos x)}{\sin x}

    =\frac{\tan x-\sin x}{\tan x\sin x}

    Grandad
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  3. #3
    Junior Member
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    Thanks!!
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