Question

1+Cosx 1-Cosx

_______ - _______ = 4CotxCscx

1-cosx 1+Cosx

Answer 1

LS = (1+cosx)/(1-cosx) - (1-cosx)/(1+cosx)

= ((1+cosx)(1+cosx) - (1-cosx)(1-cosx)/((1-cosx)(1+cosx))
= (1 + 2cosx + cos^2x - 1 + 2cosx - cos^2x)/(1-cos^2x)
= 4cosx/sin^2x
= 4(cosx/sinx)(1)/sinx
= 4cotx cscx
= RS