Question

12 If $\tan x=\frac{2t}{1-t^2}$ and $\sin y=\frac{2t}{1+t^2}$, $\frac{dy}{dx}$

Answer 1

1

Answer 2

Explanation:
Using the double angle identities, note that

$$\tan x=\frac{2t}{1-t^2}=\tan(2\arctan t) \quad\Rightarrow\quad x=2\arctan t,$$

and

$$\sin y =\frac{2t}{1+t^2}=\sin(2\arctan t) \quad\Rightarrow\quad y=2\arctan t.$$

Thus, $y=x$ and hence

$$\frac{dy}{dx}=1.$$

Answer:
$1$ (Option C if presented among multiple choices)