(sin x)/(sqrt(1+tan^(2)x))+(cos x)/(sqrt(1+cot^(2)x))

f(x)=(sin x)/(sqrt(1+tan^2x))+(cos x)/(sqrt(1+cot^2x)) is constant in which of following interval a. \ (0,\ pi/2) b. (pi/2,\ pi) c. (pi,\ (3pi)/2) d. ((3pi)/2,2pi)

The minimum value of the function f(x)=(sin x)/(sqrt(1-cos^(2)x))+(cos x)/(sqrt(1-sin^(2)x))+(tan x)/(sqrt(sec^(2)x-1))+(cot x)/(sqrt(csc^(2)x-1))

If the maximum and minimum values of (sin x)/(sqrt(1-cos^(2)))+(cos x)/(sqrt(1-sin^(2)x))+(tan x)/(sqrt(sec^(2)x-1))+(cot x)/(sqrt(cos ec^(2)-1)) when it is defined are M and m respectively then the values of M-m is

If -1

Express sin^(-1)x in terms of (i) cos^(-1)sqrt(1-x^(2)) (ii) "tan"^(-1)x/(sqrt(1-x^(2))) (iii) "cot"^(-1)(sqrt(1-x^(2)))/x

Express sin^(-1)x in terms of (i) cos^(-1)sqrt(1-x^(2)) (ii) "tan"^(-1)x/(sqrt(1-x^(2))) (iii) "cot"^(-1)(sqrt(1-x^(2)))/x

Let g(x)=sqrt(sin^(-1)(cos(tan^(-1)x))+cos^(-1)(sin(cot^(-1)x))) ,then int_(-sqrt((pi)/(2)))^(sqrt((pi)/(2)))g(x)dx equals

prove that tan^(-1)((cos x)/(1-sin x))-cot^(-1)((sqrt(1+cos x))/(sqrt(1-cos x)))=(pi)/(4),x varepsilon(0,(pi)/(2))

int(2sin x)/((3+sin2x))dx is equal to (1)/(2)ln|(2+sin x-cos x)/(2-sin x+cos x)|-(1)/(sqrt(2))tan^(-1)((sin x+cos x)/(sqrt(2)))+c(1)/(2)ln|(2+sin x-cos x)/(2-sin x+cos x)|-(1)/(2sqrt(2))tan^(-1)((sin x+cos x)/(sqrt(2)))+c(1)/(4)ln|(2+sin x-cos x)/(2-sin x+cos x)|-(1)/(sqrt(2))tan^(-1)((sin x+cos x)/(sqrt(2)))+cnone of these

If -1< x < 0 , then cos^(-1)x is equal to (a) sec^(-1)(1/ x) (b) pi-sin^(-1)sqrt(1+x^2) (c) pi+tan^(-1)(x/(sqrt(1-x^2))) (d) cot^(-1)(x/(sqrt(1-x^2))) .