Question #6b048

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Question #6b048

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Answer 1 · 2017-04-12T11:09:23

$L H S = cot 2 x$ $LHS=cot2x$

$= \frac{cos 2 x}{sin 2 x}$ $=(cos2x)/(sin2x)$

$= \frac{{cos}^{2} x - {sin}^{2} x}{2 sin x cos x}$ $=(cos^2x-sin^2x)/(2sinxcosx)$

$= \frac{\frac{{cos}^{2} x}{{cos}^{2} x} - \frac{{sin}^{2} x}{{cos}^{2} x}}{\frac{2 sin x cos x}{{cos}^{2} x}}$ $=(cos^2x/cos^2x-sin^2x/cos^2x)/((2sinxcosx)/cos^2x)$

$= \frac{1 - {tan}^{2} x}{\frac{2 sin x}{cos x}}$ $=(1-tan^2x)/((2sinx)/cosx)$

$= \frac{1 - {tan}^{2} x}{2 tan x} = R H S$ $=(1-tan^2x)/(2tanx)=RHS$

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Question #6b048

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