`=tan^(-1)((1+sin x)/(cos x))`

tan^(-1) ((1-cos x)/(sin x))

Prove that : cos^(-1) x = 2 cos^(-1) sqrt((1+x)/(2)) (ii) Prove that : tan^(-1)((cosx + sin x)/(cosx - sin x)) = (pi)/(4)+ x

y=tan^(-1)(cos x/(1+sin x))

Differentiate the following w.r.t x tan^(-1) ((cos x - sin x)/(cos x + sin x))

(v) tan^(-1)sqrt((1+cos x)/(1-cos x))

If x in (0,1) and f(x)=sec{tan^(-1)((sin(cos^(-1)x)+cos(sin^(-1)x))/(cos(cos^(-1)x)+sin(sin^(-1)x)))} , then sum_(r=2)^(10)f(1/r) is _______ .

Prove that cos (tan^(-1) (sin (cot^(-1) x))) = sqrt((x^(2) + 1)/(x^(2) + 2))

Write the simplest form : tan^-1( (cos x)/(1+sin x))

If alpha = sin^(-1) (cos(sin^-1) x)) and beta = cos^(-1) (sin (cos^(-1) x)) , then find tan alpha. tan beta.

Find the value of, cos [tan^(-1) {sin (cot^(-1)x)}]