Prove? cotx-tanx = cos2x/sinxcosx

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Prove? cotx-tanx = cos2x/sinxcosx

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Answer 1 · 2018-03-21T07:34:02

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Explanation:

We want to verify the identity

$cot (x) - tan (x) = \frac{cos (2 x)}{sin (x) cos (x)}$ $cot(x)-tan(x)=cos(2x)/(sin(x)cos(x))$

Remember the identity

$cos (2 x) = {cos}^{2} (x) - {sin}^{2} (x)$ $cos(2x)=cos^2(x)-sin^2(x)$

$R H S = \frac{cos (2 x)}{sin (x) cos (x)}$ $RHS=cos(2x)/(sin(x)cos(x))$

$R H S = \frac{{cos}^{2} (x) - {sin}^{2} (x)}{sin (x) cos (x)}$ $color(white)(RHS)=(cos^2(x)-sin^2(x))/(sin(x)cos(x))$

$R H S = \frac{{cos}^{2} (x)}{sin (x) cos (x)} - \frac{{sin}^{2} (x)}{sin (x) cos (x)}$ $color(white)(RHS)=(cos^2(x))/(sin(x)cos(x))-(sin^2(x))/(sin(x)cos(x))$

$R H S = \frac{cos (x)}{sin (x)} - \frac{sin (x)}{cos (x)}$ $color(white)(RHS)=(cos(x))/(sin(x))-(sin(x))/(cos(x))$

$R H S = cot (x) - tan (x) = L H S$ $color(white)(RHS)=cot(x)-tan(x)=LHS$

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Prove? cotx-tanx = cos2x/sinxcosx

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Explanation:

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