Consider the ellipse `x^(2)/(tan^(2)alpha)+y^(2)/(sec^(2)alpha)=1` where `alphain(0,pi/2)`. Which of the following quantities would vary as `alpha` varies?

For the hyperbola x^2/ cos^2 alpha - y^2 /sin^2 alpha = 1;(0 lt alphalt pi/4) . Which of the following remains constant when alpha varies?

if (1+tan alpha )(1+tan4 alpha ) =2 where alpha in (0 , pi/16 ) then alpha equal to

If latus recturn of the ellipse x^2 tan^2 alpha+y^2 sec^2 alpha= 1 is 1/2 then alpha(0 lt alpha lt pi) is equal to

For the hyperbola (x^2)/(cos^2alpha)-(y^2)/(sin^2alpha)=1 , which of the following remains constant when alpha varies? (1) eccentricity (2) directrix (3) abscissae of vertices (4) abscissae of foci

If cos 5 alpha=cos^5 alpha, where alpha in (0,pi/2) then find the possible values of (sec^2 alpha+cosec^2 alpha+cot^2 alpha).

Solve : tan ^(2) alpha + sec alpha - 1 = 0,0 le alpha lt 2pi.

Minimum value of (sec^4alpha)/(tan^2beta)+(sec^4beta)/(tan^2alpha), where alpha!=pi/2,beta!=pi/2 ,0

The value of expression (tan alpha+sin alpha)/(2"cos"^(2)(alpha)/(2)) for alpha=(pi)/(4) is :

Consider equation (x - sin alpha) (x-cos alpha) - 2 = 0 . Which of the following is /are true?

"If "y=sqrt((2(tanalpha+cotalpha))/(1+tan^(2)alpha)+(1)/(sin^(2)alpha))"when "alpha in ((3pi)/(4),pi)"then find "(dy)/(dalpha)" at" alpha=(5pi)/(6)