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Math Help - Verifying!!

  1. #1
    J^2
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    Exclamation Verifying!!

    1. (cos^2t)/(1-sint)= 1+sint


    2. (cot)(x/2)*sinx= 1 + cosx

    3. (2cotx)=csc^2x*sin2x

    4. (2+2cot^2x)= 2cotxsecxcscx

    5. (sinxcosx)=(cosx-cos^3x)/(sinx)

    6. 2sinA-cscA=sinA- (cotA)/(secA)

    Please help i have no idea how to do these ones... i did about 25 others and cannot for the life of me figure these ones out... please help!!!
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  2. #2
    Member Nacho's Avatar
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    Knowing

    \sin^2x+\cos^2x=1

    the number 1:

    <br />
\frac{{\cos ^2 t}}<br />
{{1 - \sin t}} = \frac{{1 - \sin ^2 t}}<br />
{{1 - \sin t}} = \frac{{\left( {1 - \sin t} \right)\left( {1 + \sin t} \right)}}<br />
{{1 - \sin t}} = 1 + \sin t<br />

    too could be usefull

    <br />
\begin{gathered}<br />
  \sin \left( {x + y} \right) = \sin x\cos y + \sin y\cos x \hfill \\<br />
  \cos \left( {x + y} \right) = \cos x\cos y - \sin x\sin y \hfill \\ <br />
\end{gathered} <br />

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  3. #3
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    Hello, J^2!

    2)\;\;\cot\tfrac{x}{2}\cdot\sin x\:=\: 1 + \cos x

    We have: . \cot\tfrac{x}{2}\;\;\cdot\;\;\sin x
    . . . . . = \;\overbrace{\frac{\cos\frac{x}{2}}{\sin\frac{x}{2  }}}\cdot\overbrace{2\sin\tfrac{x}{2}\cos\tfrac{x}{  2}}  \;=\;2\cos^2\!\tfrac{x}{2} \;=\;1 + \cos x



    3)\;\;2\cot x \:=\:\csc^2\!x\cdot\sin2x

    We have: . \csc^2\!x\;\;\cdot\;\;\sin2x

    . . . . . = \;\overbrace{\frac{1}{\sin^2\!x}}\cdot\overbrace{2  \sin x\cos x} \;=\;\frac{2\cos x}{\sin x} \;=\;2\cot x

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  4. #4
    J^2
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    THANKS!!

    Thank you guys, very much!!! I don't know why I could not figure these ones out... but i guess i am just better at the other 25... Thanks again guys!!
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