Which of the following expressions makes an identity when equated to tan (x/2)?

Question

A. + or - sqrt[(1 + cos x) / (1 - cos x)]

B. (1 + cos x) / (sin x)

C. (sin x) / (1 - cos x)

D. csc x - cot x

Answer 1

A would be true except fot the signs of cosx

B would be true except for the sign of cosx

C would be true except for the sign of cosx

D is an identity: cscx - cotx = tan(x/2) = sinx/(1+cosx)

= 1/sinx - 1/tanx = 1/sinx - cosx/sinx = (1-cosx)/sinx = sinx/(1+cosx)

=