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Math Help - Trig limit

  1. #1
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    Trig limit

    Evaluate the following limit without using l'Hopitals rule.
    \lim_{x\to\frac{\pi}{4}}\frac{6-6tanx}{sinx-cosx}

    No matter how I attempt to manipulate it I always end up with a 0 in the denominator, if anyone could help?
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  2. #2
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    Quote Originally Posted by xxlvh View Post
    Evaluate the following limit without using l'Hopitals rule.
    \lim_{x\to\frac{\pi}{4}}\frac{6-6tanx}{sinx-cosx}

    No matter how I attempt to manipulate it I always end up with a 0 in the denominator, if anyone could help?
    \frac{6-6\tan{x}}{\sin{x}-\cos{x}} =

    \frac{6(1-\tan{x})}{\sin{x}-\cos{x}} =

    \frac{6\left(\frac{\cos{x}}{\cos{x}} -\frac{\sin{x}}{\cos{x}}\right)}{\sin{x}-\cos{x}} =

    \frac{6\left(\frac{\cos{x}-\sin{x}}{\cos{x}}\right)}{\sin{x}-\cos{x}} =

    \frac{6(\cos{x}-\sin{x})}{\cos{x}(\sin{x}-\cos{x})} =

    -\frac{6}{\cos{x}}

    now find the limit
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