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Math Help - sin(y)tan(x)

  1. #1
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    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) ?
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  2. #2
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    \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}.
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