sin a + sin b = (1/2)^(1/2)                

cos a +cos b = 1,

find> tan a +tan b = ?

2 sin(a+b)/2 * cos (a-b)/2 =(1/2)^1/2

2 cos (a+b)/2 * cos (a-b)/2 =1 

now we get tan (a+b)/2  = (1/2)^1/2  

tan (a+b) =2tan(a+b)/2 /  1+tan²(a+b)/2

tan a+b  =(2)^1/2/(1/2)

tan a+b =2(2)^1/2

sina + sinb = 1/root2.

cosa + cosb = 1.

(sina)^2 + (cosa)^2 = 1 = (1/root2 - sinb)^2 + (1-cosb)^2.

1/2 + (sinb)^2 - (root2)(sinb) + 1 + (cosb)^2 - 2cosb = 1.

3/2 - root2(sinb) = 2cosb.

9/4 + 2(sinb)^2 - 3(root2)(sinb) = 4 - 4(sinb)^2.

from here we can get, sinb. then we can get all what we want easily.

if we put x = sinb then we get

or

see kartik, even if something is wrong, the procedure seems correct to me.

sorry if anything is wrong man!!!