Verify the identity sin3x sinxSolutionwe can write sin3 x

Verify the identity: sin(3-x) = sin(x)

Solution

we can write sin(3 - x) = sin((2+-x)

we know that sin(A+B)=sinAcosB+cosASinB
sin(2 + -x) =sin(2+(+-x)

= sin(2)cos(-x) + sin(-x)cos(2)

= 0*cos(-x) + sin(-x)*1

= sin(-x)
sin(-x) = sin()cos(x) - sin(x)cos()

= 0*cos(x) - sin(x)*-1

=sin(x)