Question

Prove that
$\frac{1 + \cos\alpha + \sin\alpha }{1 + \cos \alpha - \sin \alpha } = \frac{1 + \sin \alpha }{ \cos \alpha}$

Answer 1

Hey !!!

1 + cos@ + sin@
----------------------
1 + cos@ - sin@

sec@ + 1 + tan@
------------------------
sec@ + 1 - tan@

=> sec@ +tan@ + (sec²@ - tan²@)
----------------------------------------------
sec@ + 1 - tan@

=> sec@ + tan@ +1 (sec@ - tan@) (sec@+tan@)
--------------------------------------------
sec@ + 1 -tan@

=> (sec@ + tan@ ) ( sec@ - tan@ +1 )
-------------------------------------
sec@ + 1 - tan@

=> sec@ + tan@

=> 1 /cos@ + sin@ /cos@

=> 1 + sin@ /cos@ RHS prooved

Hope it helps you !!

@Rajukumar111