Evaluate $$\int {{{\sin x} \over {\sin x - \cos x}}dx} $$

Find the derivative of $$\sin \left( {{x^2} + 1} \right)$$ with respect to $$x$$ first principle.

If $$\tan \alpha = {m \over {m + 1}}\,$$ and $$\tan \beta = {2 \over {2m + 1}},$$ find the possible values of $$\left( {\alpha + \beta } \right).$$

Find the equation of the circle whose radius is 5 and which touches the circle $${x^2}\, + \,{y^2}\, - \,2x\,\, - 4y\, - 20 = 0\,$$ at the point (5, 5).