Let the function f : (0, pi) to RR be ...

Let the function `f : (0, pi) to RR ` be defined by ` f(theta = (sin theta + cos theta)^(2) +(sin theta - cos theta)^(4)` Suppose the function f has a local minimum at `theta` precisely when ` theta in { lambda_(1),pi,....,lambda_(r )pi}` , where `0 lt lambda_(1) lt ....lt lambda_(r ) lt 1 . ` Then the value of `lambda_(1)+....+lambda_(r ) ` is _______

Similar Questions

Explore conceptually related problems

If 0lt theta lt 90^(@) , the (sin theta+cos theta) is :

If 3 sin 2 theta = 2 sin 3 theta and 0 lt theta lt pi , then sin theta =

If : 0 lt theta lt pi/2 and sin 7theta + sin 4 theta + sin theta=0 , then : theta =

If z = (1+cos theta + i sin theta)/(sin theta + i(1+cos theta))(0 lt theta lt pi//2) then |z| equals

If 0 lt theta lt (pi)/(4) , then what is sqrt(1-2 sin theta cos theta) equal to ?

For -pi/2 lt theta lt pi/2, (sintheta + sin 2theta)/(1+costheta + cos2theta) lies in the interval

If sin^(6) theta + cos^(6) theta -1 = lambda sin^(2) theta cos^(2) theta then the value of lambda is

If (cos theta)/(1- sin theta) + (cos theta)/(1 + sin theta) =4 , then find the value of cos theta . Find theta if 0^(@) lt theta lt 90^(@)

if (cos theta)/(1-sin theta)+ (cos theta)/(1 + sin theta) = 4 , 0^@ lt theta lt 90^@ then what is the value of (sec theta + cosec theta + cot theta)?