Derive the identity

Question

sin2x = 2sinx cosx

Answer 1

The function is sin2x = 2sinx cosx

sin2x = sin (x + x)

Recall the trigonometry compound angles formula:  sin (A + B) = sinA cosB + cosA sinB

sin (x + x) = sinx cosx + cosx sinx

 sin (x + x) = sinx cosx + sinx cosx

 sin (x + x) = 2sinx cosx

Therefore  sin2x = 2sinx cosx