If `0 lt alpha lt pi/2` then show that `tanalpha+cotalphagtsinalpha+cosalpha`

If 0 lt x lt pi /2 then

If 0 lt x lt pi/2 then

If 0 lt alpha lt beta lt (pi)/(2) then

If 0 lt alpha lt pi/6 , then the value of (alpha cosec alpha ) is

If 0 lt x lt pi/2 show that cosxgt1- x^2/2

If 5tanalpha=4 , show that (5sinalpha-3cosalpha)/(5sinalpha+2cosalpha)=1/6

if 0ltalphaltbetaltgammaltpi/ 2, then prove that tanalpha lt (sinalpha+sinbeta+singamma)/ (cosalpha+cosbeta+cosgamma)lt tangamma

If 0 lt alpha lt (pi)/(3) , then prove that alpha (sec alpha) lt (2pi)/(3).

If 0 lt alpha, beta lt pi and they satisfy cos alpha + cosbeta - cos(alpha + beta)=3/2

If sec alpha=13/5, (0 lt alpha lt pi/2) , then the value of (2-3cotalpha)/(4-9sqrt(sec^(2)alpha-1)) is