Question

If x+y+z=π, then sinx+siny/cosx+cosy=_____. correct answer will be marked as brainliest.

Answer 1

Answer:

$cot(\frac{z}{2})$

Step-by-step explanation:

$\frac{sinx +siny}{cosx + cosy} = \frac{2 sin(\frac{x+y}{2}) cos(\frac{x-y}{2} ) }{2cos(\frac{x+y}{2})cos (\frac{x-y}{2} ) }$

               $= tan (\frac{x+y}{2})$

               $= tan(\frac{\pi-z }{2})$

               $= tan(\frac{\pi }{2}-\frac{z}{2})$

               $= cot(\frac{z}{2})$