Question

How do you simplify `sin(x+pi)`?

Answer 1

`-sinx`

Explanation:

Using `color(blue)"addition formula for sin"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(sin(A+B)=sinAcosB+cosAsinB)color(white)(a/a)|)))`

`rArrsin(x+pi)=sinxcospi+cosxsinpi`

now `cospi=-1" and " sinpi=0`

`rArrsinxcospi+cosxsinpi=-sinx+0`

`rArrsin(x+pi)=-sinx`