[" 4.If "(pi)/(2)

f(x) = {{:((k cosx )/((pi - 2x)"," if x ne (pi)/(2))),(3"," if x = (pi)/(2)):} at x = (pi)/(2) .

The value of (cos"" (pi)/(2)+isin ""(pi)/(2))(cos ((pi)/(2^2))+isin((pi)/(2^2))) (cos ((pi)/(2^3))+isin((pi)/(2^3)))" ………."oo is

sin""((pi)/2+ theta ) * cos (pi- theta ) * cot ""((3pi)/(2)+ theta ) - sin""((pi)/2- theta ) * sin""((3pi)/2 - theta ) * cot ""((pi)/2 + theta ) =

Let f(x)={{:(-2sinx" if "xle-(pi)/(2)),(Asinx+B" if "-(pi)/2ltxlt(pi)/(2)),(cosx" if " xge(pi)/(2)):} . Then

f(x)={((5^(cosx)-1)/((pi)/(2)-x)",", x ne (pi)/(2)), (log 5"," , x =(pi)/(2)):} at x =(pi)/(2) is

f(x)={((5^(cosx)-1)/((pi)/(2)-x)",", x ne (pi)/(2)), (log 5"," , x =(pi)/(2)):} at x =(pi)/(2) is

If f(x)={{:((1-sinx)/(pi-2x),,","xne(pi)/(2)),(lambda,,","x=(pi)/(2)):},"be continuous at "x=(pi)/(2), then value of lambda is

The function f(x)=tan^(-1)(sin x+cos x) is an increasing function in (-(pi)/(2),(pi)/(4))(b)(0,(pi)/(2))(-(pi)/(2),(pi)/(2))(d)((pi)/(4),(pi)/(2))

Range of tan^(-1)((2x)/(1+x^(2))) is (a) [-(pi)/(4),(pi)/(4)] (b) (-(pi)/(2),(pi)/(2))(c)(-(pi)/(2),(pi)/(4)) (d) [(pi)/(4),(pi)/(2)]

The smallest positive root of the equation tan x-x=0 lies in (0,(pi)/(2)) (b) ((pi)/(2),pi)(pi,(3 pi)/(2)) (d) ((3 pi)/(2),2 pi)