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.

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 |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)

int_0^(pi/2)sin4xcotx dx is equal to -pi/2 (2) 0 (3) pi/2 (4) pi

int_0^pi cos2xlogsinxdx= (A) pi (B) -pi/2 (C) pi/2 (D) none of these

Period of sin^2theta is- pi^2 b. pi/2 c. 2pi d. pi

The value of int_(-pi/2)^(pi/2) (sin^2x)/(1+2^x)dx is: (A) pi (B) pi/2 (C) 4pi (D) pi/4

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)]