# Math Help - sin(y)tan(x)

1. ## sin(y)tan(x)

I know this is kinda simple for you all.

If x + y = 90 degrees, then [sin (x) tan (y)] / [ sin (y) tan (x) ] is equal to

cot (x) or cot (y) ?

2. $\displaystyle x + y = 90^{\circ} \implies y = 90^{\circ} - x$.

So $\displaystyle \frac{\sin{x}\tan{y}}{\sin{y}\tan{x}} = \frac{\sin{x}\tan{(90^{\circ} - x)}}{\sin{(90^{\circ}-x)}\tan{x}}$

$\displaystyle = \frac{\sin{x}\cot{x}}{\cos{x}\tan{x}}$

$\displaystyle = \frac{\frac{\sin{x}\cos{x}}{\sin{x}}}{\frac{\sin{x }\cos{x}}{\cos{x}}}$

$\displaystyle = \frac{\cos{x}}{\sin{x}}$

$\displaystyle = \cot{x}$.