Tan of sum of two angles

Consider tan(a+b) 

Now

tanα = sinα/cosα

so tan(a+b) = sin(a+b)/cos(a+b)

= (sin(a)cos(b) + cos(a)sin(b)) / (cos(a)cos(b) - sin(a)sin(b))

(sin sum of 2 ang.s and cos sum of 2 ang.s)