With usual notations in $$\triangle$$ABC, if $$\frac{\sin A}{\sin C}=\frac{\sin (A-B)}{\sin (B-C)}$$, then $$a^2, b^2, c^2$$ are in

The general solution of the differential equation $$\cos (x+y) \frac{d y}{d x}=1$$ is

The derivative of the function $$\cot ^{-1}\left[(\cos 2 x)^{1 / 2}\right]$$ at $$x=\pi / 6$$ is

The domain of the function $$\log _{10}\left(x^2-5 x+6\right)$$ is