Question

Is `f(x)=cosx*tanx-sinx` increasing or decreasing at `x=pi/6`?

Answer 1

f(x) = 0, a constant, for all x.

Explanation:

If `f(x) = h(x)(g(x)/(h(x)))-g(x), f(x)=g(x)-g(x)=0`, when h(x) is not 0.

If `h(x)to0` as `xtoa, x=a+k and h(a+k)= l`, then as `xtoa, (h(x))/(h(x))to limkto0` of (l/l)=1...
In any case, f(x) =0.

Here, h(x) = cos x, g(x) = sin x and a= an odd multiple of `pi/2`.