If latusrectum of the ellipse `x^(2)tan^(2)alpha+y^(2)sec^(2)alpha=1` is 1/2, then `alpha(0ltalphaltpi)` is 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

If the length of the latusrectum of the ellipse x^(2) tan^(2) theta + y^(2) sec^(2) theta = 1 is 1/2, then theta =

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?

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

If cos alpha=(2cos beta-1)/(2-cos beta) then tan (alpha/2) is equal to

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

If tan alpha =m/(m+1) and tan beta =1/(2m+1) , then alpha+beta is equal to

If (pi)/(2)lt alpha lt (3pi)/(4) , then sqrt(2tan alpha+(1)/(cos^(2)alpha)) is equal to

If 0 lt alpha lt (pi)/(16) and (1+tan alpha)(1+tan4alpha)=2 , then the value of alpha is equal to

If alpha is a real root of the equation x^(2)+3x-tan2=0 then cot^(-1)alpha+"cot"^(-1)1/(alpha)-(pi)/2 can be equal to