Explanation

(b)
The equation of tangent to the given ellipse in parametric form is
$\frac{x}{5}\cos\theta + \frac{y}{3}\sin\theta = 1\ \ \ldots(i)$
But, the given equation of tangent is $\frac{3x}{15\sqrt{2}} + \frac{3y}{15\sqrt{2}} = 1\ \ldots(ii)$
Since, Eqs. (i) and (ii) represent the same line
$\ \therefore\frac{\cos\theta}{5} = \frac{3}{15\sqrt{2}}\ and\ \frac{\sin\theta}{3} = \frac{5}{15\sqrt{2}}$
$\Rightarrow \ \ \cos{\theta = \frac{1}{\sqrt{2\ }}}\ \ and\ \ \sin\theta = \frac{1}{\sqrt{2}}$
$\Rightarrow \ \theta = \frac{\pi}{4}$