Let `f(theta)=1/(1+(cottheta)^x)` , and `S=sum_(theta=1^0)^(89^0)f(theta),` then the value of `sqrt(2S-8)` is___________

f(theta)=(1)/(1+(tan theta)^(2013)), then value of sum_(theta=1^(@))^(89^(@))f(theta) equals

Let f (theta)=(1)/(1+(tan theta)^(2021)) , then the value of sum_(theta=1^(@))^(89^(@))f(theta) is equal to

f(theta)=int_0^1 (x+sin theta)^2 dx

Let f(theta)=(cot theta)/(1+cot theta) and alpha+beta=(5 pi)/(4) then the value f(alpha)f(beta) is

If: f(theta)=log((1+theta)/(1-theta)), then: f((2theta)/(1+theta^2))=

Let f(theta)=(cot theta)/(1+cot(theta)) and alpha+beta=(5 pi)/(4) then the value of f(alpha)*f(beta) is (a)1/2 (b) -1/2 (c)2(d) none of these

If sum_(r=15)^(29)cos((r pi)/(2)+theta)=S_(1) and sum_(r=15)^(29)sin((r pi)/(2)+theta)=S_(2) then find the value of (s_(2))/(s_(1))

If f(theta)=(1-sin2 theta+cos2 theta)/(2cos2 theta), then value of 8f(11^(0))*f(34^(0))^(0) is

Let f(theta)=(1+sin^(2)theta)(2-sin^(2)theta) . Then for all values of theta

Let f(theta) =int_(0)^(1) (x+ sin theta )^(2) dx and g(theta)=int_(0)^(1)(x+ cos theta )^(2) dx where theta in [0,2 pi] . The quantity f (theta) -g(theta), AA theta in the interval given in column I, is