यदि `alpha in ( 0 , pi//2)` , तो `sqrt(x^2 + x) + (tan^2 alpha)/(sqrt(x^2 +x ) )` निम्न से सदैव बड़ा या बराबर होगा

If alpha in (0, pi/2) , then sqrt(x^(2)+x)+(tan^(2)alpha)/(sqrt(x^(2)+x)) is always greater than or equal to (x != 0, -1)

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 alpha)^(2))/(sqrt(x^(2)+x)) is always greater than or equal to

If x gt 0 and alpha lt (pi)/(2) then (sqrt(x^(2) +x)+ (tan ^(2) alpha)/(sqrt(x^(2)+x))) is never less than-

If alpha in(0,(pi)/(2)), then sqrt(x^(2)+x)+(tan^(2)alpha)/(sqrt(x^(2)+x)) is always greater than or equal to (a)2tan alpha(b)1 (c) 2(d)sec2 alpha

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 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

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

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

Show that : int_(0)^(pi//2) (sqrt(tan x) +sqrt(cot x))dx=sqrt(2)pi .