If `- pi/2 < x < pi/2 and y=log_10(tanxsecx).` Then the expression `E=(10^y-10^-y)/2` simplifies to one of the six trigonometric functions, find the trigonometric function.

The argument of (1-i)/(1+i) is a. -pi/2 b. pi/2 c. (3pi)/2 d. (5pi)/2

If : f(x) {: ((1-sin x)/(pi-2x)", ... " x != pi//2 ),(=lambda ", ... " x = pi//2):} is continuous at x = pi//2 , then : lambda =

If f(x) is continuous at x = (pi)/2 , where f(x) = (sinx)^(1/(pi-2x)), "for" x != (pi)/2 , then f((pi)/(2)) =

If f(x) is continuous at x = (pi)/2 , where f(x) = (sinx)^(1/(pi-2x)), "for" x != (pi)/2 , then f((pi)/(2)) =

If |veca+vecb|lt|vecavecb| then the angle between veca and vecb lies in the interval (A) (-pi/2, pi/2) (B) (0,pi0) (C) (pi/2,(3pi)/2) (D) (0,2pi)

Let f(x) =(kcosx)/(pi-2x) if x!=pi/2 and f(x)=3 if x=pi/2 then find the value of k if lim_(x->pi/2) f(x)=f(pi/2)

which of the following statement is // are true ? (i) f(x) =sin x is increasing in interval [(-pi)/(2),(pi)/(2)] (ii) f(x) = sin x is increasing at all point of the interval [(-pi)/(2),(pi)/(2)] (3) f(x) = sin x is increasing in interval ((-pi)/(2),(pi)/(2)) UU ((3pi)/(2),(5pi)/(2)) (4) f(x)=sin x is increasing at all point of the interval ((-pi)/(2),(pi)/(2)) UU ((3pi)/(2),(5pi)/(2)) (5) f(x) = sin x is increasing in intervals [(-pi)/(2),(pi)/(2)]& [(3pi)/(2),(5pi)/(2)]

which of the following statement is // are true ? (i) f(x) =sin x is increasing in interval [(-pi)/(2),(pi)/(2)] (ii) f(x) = sin x is increasing at all point of the interval [(-pi)/(2),(pi)/(2)] (3) f(x) = sin x is increasing in interval ((-pi)/(2),(pi)/(2)) UU ((3pi)/(2),(5pi)/(2)) (4) f(x)=sin x is increasing at all point of the interval ((-pi)/(2),(pi)/(2)) UU ((3pi)/(2),(5pi)/(2)) (5) f(x) = sin x is increasing in intervals [(-pi)/(2),(pi)/(2)]& [(3pi)/(2),(5pi)/(2)]

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))

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