If y=x (a+y), then d x d y : - Vidyadip

MCQ

If $\sin y=x \cos (a+y)$, then $\frac{d x}{d y}$ :

✓
$\frac{\cos a}{\cos ^2(a+y)}$
B
$\frac{-\cos a}{\cos ^2(a+y)}$
C
$\frac{\cos a}{\sin ^2 y}$
D
$\frac{-\cos a}{\sin ^2 y}$

✓

Answer

Correct option: A.

$\frac{\cos a}{\cos ^2(a+y)}$

(A)Here $\quad x=\frac{\sin y}{\cos (a+y)}$$
\begin{aligned}
\therefore \quad \frac{d x}{d y} & =\frac{\cos (a+y) \cos y-\sin y[-\sin (a+y)}{\cos ^2(x \times y)} \\
& =\frac{\cos (a+y) \cos y+\sin (a+y) \sin y}{\cos ^2(a+y)} \\
& =\frac{\cos (a+y-y)}{\cos ^2(a+y)}=\frac{\cos y}{\cos ^2(a+y)}
\end{aligned}
$

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