Let `0 lt theta lt (pi)/2`. If the eccentricity of the hyperbola `(x^(2))/(cos^(2)theta)-(y^(2))/(sin^(2)theta)=1` is greater ten 2, then the length of its latus rectum lies in the interval,

If the eccentricity of the hyperbola (x^(2))/((1+sin theta)^(2))-(y^(2))/(cos^(2)theta)=1 is (2)/(sqrt3) , then the sum of all the possible values of theta is (where, theta in (0, pi) )

If eccentricity of the hyperbola (x^(2))/(cos^(2) theta)-(y^(2))/(sin^(2) theta)=1 is move than 2 when theta in (0,(pi)/2). Find the possible values of length of latus rectum (a) (3,oo) (b) 1,3//2) (c) (2,3) (d) (-3,-2)

Suppose 0lt thetalt(pi)/(2) if the eccentricity of the hyperbola x^(2)-y^(2) cosec^(2) theta=5 is sqrt(7) times the eccentricity of the ellipse x^(2) cosec^(2) theta+y^(2)=5 then theta is equal to ________

For some theta in(0,(pi)/(2)) ,if the eccentric of the hyperbola x^(2)-y^(2)sec^(2)theta=10 is sqrt(5) times the eccentricity of the ellipse, x^(2)sec^(2)theta+y^(2)=5 ,then the length of the latus rectum of the ellipse

If pi lt theta lt (3pi)/(2) , then find the value of sqrt((1-cos2theta)/(1+cos 2 theta)) .

If (sin 3theta)/(cos 2theta)lt 0 , then theta lies in

For -(pi)/(2)