If `alpha, beta` are the intercepts made on the axes by the tangent at any point of the curve `x = acos^3theta and y=bsin^3 theta,` prove that `alpha^2/a^2+beta^2/b^2=1.`

If x=acos^(3)theta and y = bsin^(3)theta , prove that ((x)/(a))^(2//3)+((y)/(b))^(2//3)=1.

The maximum value of the sum of the intercepts made by any tangent to the curve (a sin^(2)theta, 2a sin theta) with the axes is

The maximum value of the sum of the intercepts made by any tangent to the curve (a sin^(2)theta, 2a sin theta) with the axes is

The maximum value of the sum of the intercepts made by any tangent to the curve (a sin^(2)theta, 2a sin theta) with the axes is

If the length of the tangent drawn from (alpha,beta) to the circle x^(2)+y^(2)=6 be twice the length of the tangent from the same point to the circle x^(2)+y^(2)+3x+3y=0, then prove that alpha^(2)+beta^(2)+4 alpha+4 beta+2=0

The equation of the tangent to the curve (x/a)^(2//3)+(y/b)^(2//3)=1 at (acos^3theta,bsin^3theta) is

If alpha, beta are the roots of the equation a cos theta + b sin theta = c , then prove that cos(alpha + beta) = (a^2 - b^2)/(a^2+b^2) .

If alpha " and " beta are two distinct roots of a cos theta + b sin theta = c , prove that sin (alpha + beta) = (2ab)/(a^(2)+b^(2))

If alpha and beta are distict roots of a cos theta+b sin theta=c, prove that sin(alpha+beta)=(2ab)/(a^(2)+b^(2))

If alpha and beta be two different roots of the equation acos theta + b sin theta = c then prove that cos(alpha +beta) =(a^(2)-b^(2))/(a^(2)+b^(2))