Find the vector equation of the line passing through the point $(2,3,-5)$ and making equal angles with the co-ordinate axes.

(a) Find $\frac{d y}{d x}$, , if $(\cos x)^y=(\cos y)^x$.

OR

(b) If $\sqrt{1-x^2}+\sqrt{1-y^2}=a(x-y)$, prove that $\frac{d y}{d x}=\sqrt{\frac{1-y^2}{1-x^2}}$.

If $x=a \sin ^3 \theta, y=b \cos ^3 \theta$,then find $\frac{d^2 y}{d x^2}$ at $\theta=\frac{\pi}{4}$.

(a) Evaluate: $\int_0^\pi \frac{e^{\cos x}}{e^{\cos x}+e^{-\cos x}} d x$

OR

(b) Find: $\int \frac{2 x+1}{(x+1)^2(x-1)} d x$