For `f(x)=sin^2x ,x in (0,pi)` point of inflection is: `pi/6` (b) `(2pi)/4` (c) `(3pi)/4` (d) `(4pi)/3`

The solution(s) of the equation cos2x sin6x=cos3x sin5x in the interval [0,pi] is/are pi/6 (b) pi/2 (c) (2pi)/3 (d) (5pi)/6

The maximum value of the function f(x)=sin(x+pi/6)+cos(x+pi/6) in the interval (0,pi/2) occurs at (a) pi/(12) (b) pi/6 (c) pi/4 (d) pi/3

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)

The length of the longest interval in which the function 3sinx-4sin^3x is increasing is pi/3 (b) pi/2 (c) (3pi)/2 (d) pi

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)]

If 2|sin2alpha|=|tanbeta+cotbeta|,alpha,beta in (pi/2,pi), then the value of alpha+beta is (a) (3pi)/4 (b) pi (c) (3pi)/2 (d) (5pi)/4

If 1+sinx+sin^2x+sin^3x+oo is equal to 4+2sqrt(3),0

f(x)=sin+sqrt(3)cosx is maximum when x= pi/3 (b) pi/4 (c) pi/6 (d) 0

The sum of all the solution in [0,4pi] of the equation tanx+cotx+1=cos(x+pi/4)i s (a) 3pi (b) pi/2 (c) (7pi)/2 (d) 4pi

If cos^2 2x+2cos^2x=1,\ x in (-pi,pi), then x can take the values : +-pi/2 (b) +-pi/4 +-(3pi)/4 (d) none of these