If `-pi/2 < theta < pi/2` then `acostheta + bsectheta >= K` then `K=`

The function f(x)=tan^(-1) (sin x+ cos x) is an increasing function in (-pi/2, pi/k) , then find k.

Difference between the greatest and least values opf the function f (x) = int _(0)^(x) (cos ^(2) t + cos t +2) dt in the interval [0, 2pi] is K pi, then K is equal to:

Difference between the greatest and least values opf the function f (x) = int _(0)^(x) (cos ^(2) t + cos t +2) dt in the interval [0, 2pi] is K pi, then K is equal to:

If the area enclosed between f(x)=min (cos ^-1(cos x).cot ^-1(cot x)) and x -axis in x in(pi, 2 pi) is (pi^2)/k where k in N , then k is equal to

Let f(x) = (1-sin x)/((pi - 2x)^(2)),"where x" ne pi//2 and f(pi//2) = k . The value of k which makes f continuous at pi//2 is :

The value of int_(pi/4)^((3pi)/4)(cos x)/(1-cos x)dx is equal to (k-(pi)/(2)) then k=

If an equation of tangent to the curve, y=cos(x+y), -1I le x le 1+pi, is x+2y=k then k is equal to :

If int_(-3 pi)^(3 pi)sin^(2)theta sin^(2)(2 theta)d theta is equal to (k pi)/(4), then value of k is