cos^(-1)((cos x+sin x)/(sqrt(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

f(x)=sqrt(sin(cos x))+ln(-2cos^(2)x+3cos x+1)+e^(cos^(-1))((2sin x+1)/(2sqrt(2sin x)))

int_(0)^((pi)/(2))(cos^(2) x sin x)/(sqrt(1+cos^(2)x))dx

(cos x)/(sqrt(1+sin x))

(cos x)/(sqrt(1+sin x))

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

cos x+sin x=sqrt(2)cos x then

sqrt(3)cos x-sin x=1

sin^(2)(cos^(-1)x)+cos^(2)(sin^(-1)(sqrt(1-x^(2)))) = ________ (0ltxlt1)