If `f(x)=l n(sinx)` and `g(x)=sin^(-1)(e^(-x))` for all `x in (0,pi)` and `f(g(alpha))=b` and `(f(g(x))'` at `x=alpha` is a then which is true.

If f(x)=ln(sin x) and g(x)=sin^(-1)(e^(-x)) for all x in(0,pi) and f(g(alpha))=b and (f(g(x))' at x=alpha is a then which is true.

If f(x)=sin(sinx) an f f'(x) +tan xf'(x)+g(x)=0 , then g(x) is :

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 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'(sin x)lt0 and f''(sin x) gt0 forall x in (0,(pi)/(2)) and g(x) =f(sinx)+f(cosx) which of the following is true?

Let f (x) = log _e (sinx ), ( 0 lt x lt pi ) and g(x) = sin ^(-1) (e ^(-x)), (x ge 0) . If alpha is a positive real number such that a = ( fog)' ( alpha ) and b = (fog ) ( alpha ) , then

If f(x)=sin x and g(x)=f(f(f,.....(f(x)))) then value of g'(0)+g''(0)+g'''(0) equals