Question

Sum and difference tan(135+30)

Answer 1

`\tan(x+y)=(\sin(x+y))/(\cos(x+y))=(\sin x\cos y+\sin y\cos x)/(\cos x\cos y-\sin x\sin y)=(\tan x+\tan y)/(1-\tan x\tan y)`

So,


`\tan(135^\circ+30^\circ)=(\tan135^\circ+\tan30^\circ)/(1-\tan135^\circ\tan30^\circ)`

You should know that
`\tan135^\circ=-1` and
`\tan30^\circ=\frac1{\sqrt3}`

Putting everything together,


`\tan(135^\circ+30^\circ)=\frac{-1+\frac1{\sqrt3}}{1-(-1)\left(\frac1{\sqrt3}\right)}=(1-\sqrt3)/(\sqrt3+1)=\sqrt3-2`