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Write tanØ in terms of cosØ.

 Mar 11, 2020
 #1
avatar+21827 
+1

Trig identity:

 

tan2(x)=    ( 1-cos(2x) )  / ( 1+cos(2x) ) ​

 Mar 11, 2020
 #2
avatar+24371 
+2

Write \(tan^2(\phi)\) in terms of \(cos(\phi)\).

 

\(\begin{array}{|rcll|} \hline \sin^2(\phi)+\cos^2(\phi) &=& 1 \quad & | \quad : \cos^2(\phi) \\\\ \dfrac{\sin^2(\phi)}{\cos^2(\phi)}+ \dfrac{\cos^2(\phi)}{\cos^2(\phi)} &=& \dfrac{1}{\cos^2(\phi)} \\\\ \tan^2(\phi) + 1 &=& \dfrac{1}{\cos^2(\phi)} \\ \mathbf{ \tan^2(\phi) } &=& \mathbf{\dfrac{1}{\cos^2(\phi)} -1} \\ \hline \end{array} \)

 

laugh

 Mar 12, 2020
edited by heureka  Mar 12, 2020

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