Originally Posted by

**sunmalus** Hello everyone, I came across an old trigonometry problem which I'm not able to solve again and it's driving me crazy, here it is:

find the value of tan(x+y) knowing that:

tan(x)=-sqrt(2)/2

sin(y)=cos(y/2) with 19pi/4<=y<=5pi ( y in [19pi/4;5pi] ).

The final answer should be tan (x+y)= sqrt(2)-3.

My only problem is that I've a really hard time to find y. I tried to add pi/2 on both side to have cos or sin on both sides but it didn't help then I tried with a variable, pi/3=a => sin(3a)=cos(a) => sin(a)(4cosˆ2(a)-1)=cos(a) but then again it led me to nothing...

Can you please explain to me how to find y.

( I did the problem backwards and you should fin tan(y)=1-sqrt(2)).

Thanks in advance!!