If `f(x)=cos^(2)x*e^(tan x),x in(-(pi)/(2),(pi)/(2))` ,then

If f(x)=e^(x)+int_(0)^(sin x)(e^(t)dt)/(cos^(2)x+2t sin x-t^(2))AA x in(-(pi)/(2),(pi)/(2)),then

If f(x)=(e^(x)+e^(-x)-2)/(x sin x) , for x in [(-pi)/(2), (pi)/(2)]-{0} , then for f to be continuous in [(-pi)/(2), (pi)/(2)], f(0)=

If f'(x) = tan^(-1)(Sec x + tan x), x in (-pi/2 , pi/2) and f(0) = 0 then the value of f(1) is

f(x)=tan x,x in(-(pi)/(2),(pi)/(2)) and g(x)=sqrt(1-x^(2)) then g(f(x)) is

If f(x) =sin x +log_(e)|sec x + tanx|-2x for x in (-(pi)/(2),(pi)/(2)) then check the monotonicity of f(x)

Prove that tan^(-1)((cos x)/(1+sin x))=(pi)/(4)-(x)/(2),|x in(-(pi)/(2),(pi)/(2))

If f (x) = sqrt(cos ec ^(2) x - 2 sin x cos x - (1)/(tan ^(2) x )) x in ((7pi)/(4), 2pi ) then f' ((11 pi)/(6))=

Given f'(x) = (cos x )/( x ), ,f ((pi)/(2)) =a, f ((3pi)/(2))=b. Find the vlaue of the definite integral int _( pi//2) ^(3pi//2) f (x) dx.

For f(x)=(k cos x)/(pi-2x), if x!=(pi)/(2),3, if x=(pi)/(2) then find the value of k so that f is continous at x=(pi)/(2)