PLZ try this .......................

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®µD®A (2710)

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$http://latex.codecogs.com/gif.latex?(\tan%204A+\tan%202A)(1-\tan^22A\tan^2A)\\\\%20=\left(\frac{\sin4A}{\cos4A}+\frac{\sin2A}{\cos2A}\right)\left(1-\frac{\sin^23A\sin^22A}{\cos^23A\cos^2A}\right)\\\\%20=\left(\frac{\sin4A\cos2A+\cos4A\sin2A}{\cos4A\cos2A}\right)\left(\frac{\cos^2(3A)\cos^2(A)-\sin^2(3A)\sin^2(A)}{\cos^2(3A)\cos^2(A)}\right)\\\\%20=\frac{\sin%206A}{\cos%204A\cos%202A}\cdot\frac{\cos^23A\cos^22A-\sin^23A\sin^2A}{\cos^23A\cos^2A}\\\\%20=\frac{\sin%206A}{\cos%204A\cos%202A}\cdot\frac{(\cos%203A\cos%20A-\sin%203A\sin%20A)(\cos%203A\cos%20A+\sin%203A\sin%20A)}{\cos^23A\cos^2A}\\\\%20=\frac{2\sin%203A\cos%203A}{\cos%204A\cos%202A}\cdot\frac{\cos%204A\cos%202A}{\cos^23A\cos^2A}\\\\%20=2\tan%203A\cdot\frac{1}{\cos^2A}\\\\%20=2\tan%203A\sec^2A\\\\$

[IMG]http://alt1.artofproblemsolving.com/Forum/latexrender/pictures/0/6/3/0638cc54ee34d87aa803d78fe3ec072aa8749bf5.gif[/IMG] :)

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