Show that `2 sin x + tanx ge 3x ,` where ` 0 le x lt (pi)/(2)`

Show that 2sin x+tan x>=3x where 0

Show that 2sin x+tan x>=3x, where0<=x<(pi)/(2)

If : sin x +cos x = sin 2 x + cos 2 x , "where" 0 lt x le (pi)/(2), "then x":=

If : sin 5x + sin 3x + sin x = 0 , where 0 lt x le (pi)/2 , then : x =

Solve 2 cos^(2) x+ sin x le 2 , where pi//2 le x le 3pi//2 .

Let f (x) = {{:((1+sin x )",", when, 0 le x lt (pi)/(2)), (" " 1",", when, x lt 0 ):} Show that f ' (0) does not exist.

Principal solutions of the equation sin 2x + cos 2x =0 . Where pi lt x lt 2pi are

{:(f(x) = cos x and H_(1)(x) = min{f(t), 0 le t lt x},),(0 le x le (pi)/(2) = (pi)/(2)-x,(pi)/(2) lt x le pi),(f(x) = cos x and H_(2) (x) = max {f(t), o le t le x},),(0 le x le (pi)/(2) = (pi)/(2) - x","(pi)/(2) lt x le pi),(g(x) = sin x and H_(3)(x) = min{g(t),0 le t le x},),(0 le x le (pi)/(2)=(pi)/(2) - x, (pi)/(2) le x le pi),(g(x) = sin x and H_(4)(x) = max{g(t),0 le t le x},),(0 le x le (pi)/(2) = (pi)/(2) - x, (pi)/(2) lt x le pi):} Which of the following is true for H_(3) (x) ?