If `alpha in (0,pi/2),t h e nsqrt(x^2+x)+(tan^2alpha)/(sqrt(x^2+x))` is always greater than or equal to `2tanalpha` `1` `2` `sec^2alpha`

If alpha in (0,pi/2) , then sqrt(x^2+x)+tan^2alpha/sqrt(x^2+x) is always greater than or equal to (a) 2tanalpha (b)1 (c) 2 (d) sec2alpha

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

Let a in (0,(pi)/(2)) and f(x)=sqrt(x^(2)+x)+(tan^(2)alpha)/(sqrt(x^(2)+x)), x gt 0 . If the least value of f(x) is 2sqrt3 , then alpha is equal to

If alpha is an acute angle and sin(alpha/2)=sqrt((x-1)/(2x)) then tan alpha is

If 0 < alpha < pi/6 and sin alpha + cos alpha =sqrt(7 )/2, then tan alpha/2 is equal to

Let alpha in (0, pi/2) be fixed. If the integral int(tan x + tan alpha)/(tan x - tan alpha)dx = A(x)cos 2 alpha+B(x) sin 2 alpha +C ,where C is a constant of integration, then the functions A(x) and B(x) are respectively.

The value of alpha in [0,2pi] so that x^(2)+y^(2)+2sqrt(sin alpha )x+(cos alpha-1)=0 having intercept on x-axis always greater than 2, is/are

If tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))}=alpha, then prove that x^2=sin2alpha

If tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))}=alpha, then prove that x^2=sin2alpha

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