Question

Prove the identity. `sin(pi+x)=-sinx` Have to show the statements and the rules?

Answer 1

Use the sine angle sum formula:

`sin(color(red)A+color(blue)B)=sincolor(red)Acoscolor(blue)B+coscolor(red)Asincolor(blue)B`

Here's the problem:

`sin(color(red)pi+color(blue)x)=sincolor(red)picoscolor(blue)x+coscolor(red)pisincolor(blue)x`

`color(white)(sin(pi+x))=0*coscolor(blue)x+ -1*sincolor(blue)x`

`color(white)(sin(pi+x))=color(red)cancelcolor(black)(0*coscolor(blue)x)+color(red)(-1)*sincolor(blue)x`

`color(white)(sin(pi+x))=color(red)(-1)*sincolor(blue)x`

`color(white)(sin(pi+x))=-sincolor(blue)x`

That's the proof. Hope this helped!