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Math Help - Proving Trigonmetric Identity

  1. #1
    s3a
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    Proving Trigonmetric Identity

    Can someone please prove the following for me with detailed steps so I can understand?:

    cot P + tan P = (cosec P)(sec P)

    Any help would be greatly appreciated!
    Thanks in advance!
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  2. #2
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    Quote Originally Posted by s3a View Post
    Can someone please prove the following for me with detailed steps so I can understand?:

    cot P + tan P = (cosec P)(sec P)

    Any help would be greatly appreciated!
    Thanks in advance!
    \cot{\theta} + \tan{\theta} = \frac{1}{\tan{\theta}} + \tan{\theta} = \frac{1+ \tan^2{\theta}}{\tan{\theta}} = \frac{1 + \left( \frac{\sin{\theta}}{\cos{\theta}} \right) ^2 }{ \frac{\sin{\theta}}{ \cos{\theta}}}

    I think this is more than enough help, you should finish the problem for yourself.

    Hope this helped,
    pomp.
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  3. #3
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    Here's another way to do it:
    \cot P + \tan P
    \begin{aligned}<br />
&= \frac{\cos P}{\sin P} + \frac{\sin P}{\cos P} \\<br />
&= \frac{\cos^2 P}{\sin P \cos P} + \frac{\sin^2 P}{\sin P \cos P} \\<br />
&...<br />
\end{aligned}

    I'll let you figure out the rest.


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