If f(x)`=sin x-a sin 2x-(1)/(3) sin 3x+2ax` is an increasing function for all real values of x, show that, `a gt 1`.

If f(x)= x^(3) + ax^(2) + bx + c is an increasing function for all real values of x then-

If the function f(x)=(a sin x+2 cos x)/(sin x + cos x) is strictly increasing for all values of x, then a gt k , find k.

Find the condition so that the function f(x)=x^(3)+ax^(2)+bx+c is an increasing function for all real values of x.

Let f(x) be a function such that f'(x)=log_(1/3) [log_(3)(sin x+a)] . If f(x) is decreasing for all real values of x then a gt k , find k.

(sin x - sin 3x)/( sin ^(2) x - cos ^(2) x) = 2 sin x

The function f(x) = ax + b is strictly increasing for all real x if

If 2f(x) + 3f(-x) = 15 - 4x for all real values of x , then show that f(x) = 3 + 4x.

The trigonometric equation sin^(-1)x=2sin^(-1)a has a solution for all real values

Range of f(x) = (sin^2x + sin x -1)/(sin^2x - sin x + 2)

Show that f(x)=tan^(-1)(cos x+sin x) is a stictly increasing function in the interval (0, pi/4) .