" 9."cos x sqrt(1-cos2x)

If x in (pi, 2pi) , prove that ((sqrt(1+cosx))+(sqrt(1-cos x)))/((sqrt(1+cos x)) -sqrt(1-cos x)) = cot(pi/4 +x/2)

If pi

tan^(-1){(sqrt(1+cos x)+sqrt(1-cos x))/(sqrt(1+cos x)-sqrt(1-cos x))}

Prove that: (i)tan^(-1){(sqrt(1+cos x)+sqrt(1-cos x))/(sqrt(1+cos x)-sqrt(1-cos x))}=(pi)/(4)+(x)/(2)

Simplest form of tan^(-1)((sqrt(1+cos x)+sqrt(1-cos x))/(sqrt(1+cos x)-sqrt(1-cos x))), pi lt x lt (3 pi)/(2) is:

Prove that: tan^(^^)(-1){(sqrt(1+cos x)+sqrt(1-cos x))/(sqrt(1+cos x)-sqrt(1-cos x))}=pi/4-x/2, if pi

lim_(x rarr0)(1-cos x sqrt(cos2x))/((e^(x)^^2-1))

Differentiate the following with respect to x. y= sqrt(1-cos2x/(1+cos2x))