Question

Differentiate this y = 1 - cos^2 x

Answer 1

Taking differential with respect to x on both sides d/dx y =d/dx(1-cos^2x) dy/dx = d/dx1 -d/dx(cosx)^2 dy/dx =0 - 2cosx *d/dx cosx. dy/dx= -2cosx*(-sinx) d/dx x dy/dx=2sinxcosx *1 dy/dx=sin2x [d/dx (x) =1] by first principle

Answer 2

y = 1 - cos^2 x
y = 1 - (cos x)^2

dy/dx = -2cosx (-sinx)
= 2 sinx cosx
or sin (2x)