Use a graphing calculator to make a conjecture as to whether

Use a graphing calculator to make a conjecture as to whether each equation is an identity. 16) sin 2x = 2sin x cos x A) Identity B) Not an Identity

Solution

sin2x = 2*sinx*cosx

LHS : sin2x = sin(x+x)

[ by addition identity , sin(A+B) = sinA*cosB + cosA*sinB]

= sinx *cosx + cosx*sinx

= 2*sinx*cosx

hence sin2x = 2*sinx*cosx is an identity.