An extremum value of the function `f(x)=(a r csinx)^3+(a r ccosx)^3` is `(7pi^3)/8` (b) `(pi^3)/8` (c) `(pi^3)/(32)` (d) `(pi^3)/(16)`

Range of function f(x)=arccot(2x-x^(2)) is [(pi)/(4),(3 pi)/(3)](b)[0,(pi)/(4)][0,(pi)/(2)] (d) [(pi)/(4),pi]

The least and the greatest values of (sin^(-1)x)^(3)+(cos^(-1)x)^(3) are (a) (-pi)/(2),(pi)/(2) (b) (-pi^(3))/(8),(pi^(3))/(8)(c)(pi^(3))/(32),(7 pi^(3))/(8) (d) none of these

The value of sin^(-1)(cos(33pi)/5) is (3pi)/5 (b) pi/(10) (c) pi/(10) (d) (7pi)/5

Show that function f(x)=sin(2x+(pi)/(4)) is decreasing on ((3 pi)/(8),(5 pi)/(8))

The value of a for which the function f(x)=a sin x+((1)/(3))sin3x has an extremum at x=(pi)/(3) is 1(b)-1(c)0(d)2

In a right angled triangle the hypotenuse is 2sqrt(2) xx the perpendicular drawn from the opposite vertex.Then the other acute angles of the triangle are (a) (pi)/(3)and(pi)/(6) (b) (pi)/(8)and(3 pi)/(8) (c) (pi)/(4) and (pi)/(4) (d) (pi)/(5) and (3 pi)/(10)

The value of c in Lagranges theorem for the function f(x)=log sin x in the interval [(pi)/(6),(5 pi)/(6)] is (pi)/(4) (b) (pi)/(2)(2 pi)/(3) (d) none of these

Show that the function f(x)=sin(2x+pi/4) is decreasing on (3 pi/8,5 pi/8)

An extremum of the function f(x)=(2-x)/(pi)cos pi(x+3)+(1)/(pi^(2))sin pi(x+3),0x<4 occurs at x=1 (b) x=2x=3 (d) x=pi

The value of cos^(-1)(cos(5pi)/3)+sin^(-1)(sin(5pi)/3) is pi/2 (b) (5pi)/3 (c) (10pi)/3 (d) 0