Question

show work. Help me please!
sin(x-pi/4)=sqrt 2/2(sin x-cos x)

Answer 1

use the difference expansion for sin

sin(A - B) = sin(A)cos(B) - cos(A)sin(B)

you have A = x and B = pi/4

Answer 2

you you'll find you have some exact values... cos(pi/4) and sin(pi/4)

Answer 3

\[R.H.S=\sin x ~*\frac{ \sqrt{2} }{ 2 }-\cos x~*\frac{ \sqrt{2} }{ 2 }=\sin x ~\cos \frac{ \pi }{ 4 }-\cos x~\sin \frac{ \pi }{ 4 }\]
=sin ?

Answer 4

thank you!

Answer 5

you are welcome.