If `x in(0,pi/2)` then show that `2x/pi < sin x < x`.

If f(x) =tan , x in [0.(pi)/(5)] then show that (pi)/(5) lt ((pi)/(5)) lt (2pi)/(5)

If f(x)= cos [ pi^(2)] x+ cos[ -pi^(2)] x where [x] denotes the greatest integer function, then show that f(-pi)=0

If x in [0,2pi]" then "y_(1)=(sin x)/(|sin x|), y_(2)=(|cos x|)/(cos x) are identical functions for x in : I. (0,pi/2)" "II. (pi/2, pi)," "III. (pi,(3pi)/(2))," "IV. ((3pi)/(2),2pi)

If x in [0,2pi]" then "y_(1)=(sin x)/(|sin x|), y_(2)=(|cos x|)/(cos x) are identical functions for x in : I. (0,pi/2)" "II. (pi/2, pi)," "III. (pi,(3pi)/(2))," "IV. ((3pi)/(2),2pi)

Show that f(x)=log sin x is increasing on (0,pi/2) and decreasing on (pi/2,pi).

Show that f(x)=sin x is increasing on (0,pi/2) and decreasing on (pi/2,pi) and neither increasing nor decreasing in (0,pi)

Show that f(x)=sin x on [0, pi/2] functions are injective.

If x in [0. (pi)/(2)], y in [0, (pi)/(2)] and sin x + cos y =2, then the value of x+y is equal to........ A) 2pi B) pi C) pi/4 D) pi/2