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How to solve trigonometric equations by just looking at the form...

For e.g., proving $$\cos A - \sin A + \dfrac {1}{\cos A + \sin A} - 1 = \csc A + \cot A$$

First of all I know the LHS is in basic T-ratio so I don't need to convert them but if I divide LHS by $\cos A$ it changes to $\tan A$ and $\csc A$. How do I solve questions like these which have + - pattern?

Although I did it but I want to do some other way as well.

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    $\begingroup$ Please reformat your equations with MathJax so that we know exactly what you're talking about in the equations (mainly the division) $\endgroup$ – Matti P. Jan 3 at 8:05
  • $\begingroup$ math.stackexchange.com/questions/426981/… $\endgroup$ – lab bhattacharjee Jan 3 at 8:10
  • $\begingroup$ Please check this link to learn how to use MathJax. $\endgroup$ – KM101 Jan 3 at 8:20

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