Question

prove that sin (45°+A) - sin (45°-A) = √2 sinA​

Answer 1

Step-by-step explanation:

sin(A+B)=sinAcosB+cosAsinB

sin(A-B)=sinAcosB-cosAsinB

Now, sin (45°+A) - sin (45°-A)

=sin45cosA+cos45sinA-(sin45cosA-cos45sinA)

=(1/√2)cosA+(1/√2)sinA-(1/√2)cosA+(1/√2)sinA

=2(1/√2)sinA

=√2sinA