If `sin theta =a ` has exactly 3 solution in `theta in [0,(7pi)/(3)]` then the value of 'a' is

If sin theta=a for e xactly one value of theta in[0,(7 pi)/(3)], then 10, then the value of a is

If equation sin^(-1) (4 sin^(2)theta + sin theta) + cos^(-1) (6 sin theta - 1) = (pi)/(2) has 10 solution for theta in [0, n pi] , then find the minimum value of n

If equation sin^(-1) (4 sin^(20 theta + sin theta) + cos^(-1) (6 sin theta - 1) = (pi)/(2) has 10 solution for theta in [0, n pi] , then find the minimum value of n

If equation sin^(-1) (4 sin^(2)theta + sin theta) + cos^(-1) (6 sin theta - 1) = (pi)/(2) has 10 solution for theta in [0, n pi] , then find the minimum value of n

If the equation sec theta+cos ec theta=k,(k in R) has exactly 3 solution between 0 and pi, then k can take value

If f( theta ) = sin ^(3)theta + sin ^(3)( theta + (2pi)/(3)) + sin ^(3)( theta + (4pi)/(3)) then the value of f((pi)/(18)) + f((7pi)/(18)) is ___________.

If f( theta ) = sin ^(3)theta + sin ^(3)( theta + (2pi)/(3)) + sin ^(3)( theta + (4pi)/(3)) then the value of f((pi)/(18)) + f((7pi)/(18)) is ___________.

If f( theta ) = sin ^(3)theta + sin ^(3)( theta + (2pi)/(3)) + sin ^(3)( theta + (4pi)/(3)) then the value of f((pi)/(18)) + f((7pi)/(18)) is ___________.

If 1+sin^(2)theta=3sin theta cos theta then the solution set in(0,(pi)/(2)) is

If f(theta)=|sinthetacosthetasinthetacosthetasinthetacosthetacosthetasinthetasintheta| , then f(theta)=0 has exactly 2 real solutions in [0,pi] f(theta)=0 has exactly 3 real solutions in [0,pi] range of function (f(theta))/(1-sin2theta)i s[-sqrt(2),sqrt(2)] range of function (f(theta))/(sin2theta-1)i s[-3,3]