Tangent is drawn to ellipse `(x^2)/(27)+y^2=1` at `(3sqrt(3)costheta,sintheta)` [where `theta in (0,pi/2)]` Then the value of `theta` such that sum of intercepts on axes made by this tangent is minimum is (a) `pi/3` (b) `pi/6` (c) `pi/8` (d) `pi/4`

sqrt(3)tantheta tan(theta + pi/3) tan(theta + (2pi)/3) =1

A tangent is drawn at the point (3 sqrt(3) cos theta, sin theta) (0 lt theta lt (pi)/(2)) to the ellipse x^(2) + 27y^(2)=27 , then the least value of the sum of the intercepts on the coordinate axes by this tangent is attained when the value of theta is-

For all theta in [0,pi/2] show that cos(sintheta)gtsin(costheta)

costheta - sintheta = 1/sqrt(2) (-pi lt theta lt pi)

If 0 lt theta lt pi, then minimum value of 3sintheta+cosec^3 theta is

The minimum value of costheta+sintheta+2/(sin2theta) for theta in (0,pi/2) is

Prove that: (costheta)/(1+sintheta)=tan(pi/4-theta/2)

If the equation x^3+b x^2+c x+1=0,(b (a) -pi (b) -pi/2 (c) pi/2 (d) pi

The angle between the tangents to the curve y=x^2-5x+6 at the point (2, 0) and (3, 0) is (a) pi/2 (b) pi/3 (c) pi (d) pi/4

Evaluate: int_((pi)/(4))^((3pi)/(4))(costheta)/(1+sintheta)d theta