Correct option is A. \( \frac{\cos^2(a + y)}{\cos(a)}\)
\(x = \frac{\sin y}{\cos(a + y)}\)
\(\frac {dx}{dy} = \frac{\cos(a + y)\cos (y) - \sin(y) [-\sin (a + y)]}{[\cos (a + y)]^2}\)
\(\frac {dx}{dy} = \frac{\cos(a + y)\cos (y) +\sin(a + y) \sin(y) }{\cos^2 (a + y)}\)
\(\frac {dx}{dy}=\frac {\cos[(a + y)-y] }{\cos^2 (a + y)}\)
⇒ \(\frac{dy}{dx} = \frac{\cos^2(a + y)}{\cos(a)}\)