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![[Post New]](/templates/default/images/icon_minipost_new.gif) 5 Jul 2008 17:21:56 IST
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Find the range of f(x)
f(x)= sinx/(1+tan2x)1/2 - cosx/(1+cot2x)1/2
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LIFE IS A DREAM FOR ME.......... |
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6 Jul 2008 14:02:28 IST
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![\frac{\sin x}{\sqrt{1+\tan^2 x}}-\frac{\cos x}{\sqrt{1+\cot^2 x}}\\\\\frac{\sin x}{\sqrt{\sec^2 x}}-\frac{\cos x}{\sqrt{\csc ^2 x}}\\\\Case\;1:\;-\\\\f(x)=\sin x.\cos x-\cos x\sin x=0\\\\Case\;2:\;-\\\\f(x)=\sin x.\cos x+\sin x.\cos x=\sin 2x\\\\hence\;\;-1\;\le\;f(x)\;\le\;1\\\\Case\;3:\;-\\\\f(x)=\;-\sin x.\cos x-\sin x.\cos x=\;-\sin 2x\\\\hence\;\;-1\;\le\;f(x)\;\le\;1\\\\Case\;4:\;-\\\\f(x)=\;-\sin x.\cos x+\sin x.\cos x\;=\;0\\\\hence\;,\;f(x)\;\in\;[-1,1]](http://alt2.artofproblemsolving.com/Forum/latexrender/pictures/9/c/4/9c4ed2d26c2612d328d66637de216453709d93f8.gif)
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