Let `f(x)=sin[pi/6sin(pi/2sinx)]` for all `x in RR`

Let f(x) = sin (pi/6 sin (pi/2 sinx)) for all x inR and g(x) = pi/2 sinx for all x in R . Let (fog)(x) dentoe f(g(x)) and (gof)(x) denote g(f(x)). Then which of the following is (are) True?

Let f(x)=sin((pi)/6sin((pi)/2 sin x)) for all x epsilonR and g(x)=(pi)/2sinx for all x epsilonR . Let (fog) (x) denote f(g(x)) and (g o f) denote g(f(x)). Then which the following is (are) true?

Let f(x) = sin ""((pi)/(6) sin""((pi)/(2) sin x )) for all x in R and g(x) =(x)/(2) ""sin x for all x in RR .Let ( fo g) (x) denote f(g(x)) and (go f) (x) denote g(f(x)) . Then which of the following is ( are ) true ?

Let f:(0,pi) rarr R be a twice differentiable function such that lim_(t rarr x) (f(x)sint-f(t)sinx)/(t-x) = sin^(2) x for all x in (0,pi) . If f((pi)/(6))=(-(pi)/(12)) then which of the following statement (s) is (are) TRUE?

Let f(x)={-2sin x for -pi<=x<=-(pi)/(2)a sin x+b for -(pi)/(2)

Consider a function f defined by f(x)=sin^(-1) sin ((x+sinx)/2) AA x in [0,pi] which satisfies f(x)+f(2pi-x)=pi AA x in [pi, 2pi] and f(x)=f( 4pi-x) for all x in [2pi,4pi] then If alpha is the length of the largest interval on which f(x) is increasing, then alpha =

The gratest value of the function f(x)=(sinx)/(sin(x+pi/4)) on thhe interval [0,pi//2] is

f(x) = sinx - sin2x in [0,pi]