Prove the identity: sin(pi+x) = - sinx?

Question

Please show your work. Thanks for your help! :)

Answer 1

sin(pi+x) .......................................................................... - sinx
= sin pi cos x + cos pi sin x
= 0cos x + (-1)sin x
= - 1 sinx
= - sin x

Therefore, left side = right side

Answer 2

Use the identity

Sin(A+B) = SinACosB + CosASinB

where A = pi (B=x)

and Sin(pi) = 1 while Cos(pi)=-1

Answer 3

we know the formula
sin(a+b)=(sin a *cos b) + (cos a * sin b)
in the same way
sin(pi + x)=(sin pi * cos x) +(cos pi * sin x)-------1

also the value of
sin pi= 0
cos pi= -1

substitute these values in eq.1
sin(pi + x)=(0 * cos x) +((-1) * sin x)
=0+(-sin x)
=-sin x.

hence proved
here * refers to multiplication.