Simplify the expression:? $\frac{{sin}^{2} (\frac{π}{2} + α) - {cos}^{2} (α - \frac{π}{2})}{t g^{2} (\frac{π}{2} + α) - c t g^{2} (α - \frac{π}{2})}$ $(sin^2(pi/2+alpha)-cos^2(alpha-pi/2))/(tg^2(pi/2+alpha)-ctg^2(alpha-pi/2))$

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Simplify the expression:? $\frac{{sin}^{2} (\frac{π}{2} + α) - {cos}^{2} (α - \frac{π}{2})}{t g^{2} (\frac{π}{2} + α) - c t g^{2} (α - \frac{π}{2})}$ $(sin^2(pi/2+alpha)-cos^2(alpha-pi/2))/(tg^2(pi/2+alpha)-ctg^2(alpha-pi/2))$

$\frac{{sin}^{2} (\frac{π}{2} + α) - {cos}^{2} (α - \frac{π}{2})}{t g^{2} (\frac{π}{2} + α) - c t g^{2} (α - \frac{π}{2})}$ $(sin^2(pi/2+alpha)-cos^2(alpha-pi/2))/(tg^2(pi/2+alpha)-ctg^2(alpha-pi/2))$

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Answer 1 · 2017-04-10T08:58:17

$\frac{{sin}^{2} (\frac{π}{2} + α) - {cos}^{2} (α - \frac{π}{2})}{{tan}^{2} (\frac{π}{2} + α) - {cot}^{2} (α - \frac{π}{2})}$ $(sin^2(pi/2+alpha)-cos^2(alpha-pi/2))/(tan^2(pi/2+alpha)-cot^2(alpha-pi/2))$

$= \frac{{sin}^{2} (\frac{π}{2} + α) - {cos}^{2} (\frac{π}{2} - α)}{{tan}^{2} (\frac{π}{2} + α) - {cot}^{2} (\frac{π}{2} - α)}$ $=(sin^2(pi/2+alpha)-cos^2(pi/2-alpha))/(tan^2(pi/2+alpha)-cot^2(pi/2-alpha))$

$= \frac{{cos}^{2} (α) - {sin}^{2} (α)}{{cot}^{2} (α) - {tan}^{2} (α)}$ $=(cos^2(alpha)-sin^2(alpha))/(cot^2(alpha)-tan^2(alpha))$

$= \frac{{cos}^{2} (α) - {sin}^{2} (α)}{\frac{{cos}^{2} (α)}{{sin}^{2} (α)} - \frac{{sin}^{2} (α)}{{cos}^{2} (α)}}$ $=(cos^2(alpha)-sin^2(alpha))/(cos^2(alpha)/sin^2(alpha)-sin^2(alpha)/cos^2(alpha))$

$= \frac{{cos}^{2} (α) - {sin}^{2} (α)}{\frac{{cos}^{4} (α) - {sin}^{4} (α)}{{sin}^{2} (α) {cos}^{2} (α)}}$ $=(cos^2(alpha)-sin^2(alpha))/((cos^4(alpha)-sin^4(alpha))/(sin^2(alpha)cos^2(alpha)))$

$= \frac{{cos}^{2} (α) - {sin}^{2} (α)}{{cos}^{4} (α) - {sin}^{4} (α)} \times \frac{{sin}^{2} (α) {cos}^{2} (α)}{1}$ $=(cos^2(alpha)-sin^2(alpha))/(cos^4(alpha)-sin^4(alpha))xx(sin^2(alpha)cos^2(alpha))/1$

$= \frac{{cos}^{2} (α) - {sin}^{2} (α)}{({cos}^{2} (α) - {sin}^{2} (α)) ({cos}^{2} (α) + {sin}^{2} (α)) \times \frac{{sin}^{2} (α) {cos}^{2} (α)}{1}}$ $=(cos^2(alpha)-sin^2(alpha))/((cos^2(alpha)-sin^2(alpha))(cos^2(alpha)+sin^2(alpha))xx(sin^2(alpha)cos^2(alpha))/1$

$= {sin}^{2} (α) {cos}^{2} (α)$ $=sin^2(alpha)cos^2(alpha)$

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Simplify the expression:? $\frac{{sin}^{2} (\frac{π}{2} + α) - {cos}^{2} (α - \frac{π}{2})}{t g^{2} (\frac{π}{2} + α) - c t g^{2} (α - \frac{π}{2})}$ $(sin^2(pi/2+alpha)-cos^2(alpha-pi/2))/(tg^2(pi/2+alpha)-ctg^2(alpha-pi/2))$

$\frac{{sin}^{2} (\frac{π}{2} + α) - {cos}^{2} (α - \frac{π}{2})}{t g^{2} (\frac{π}{2} + α) - c t g^{2} (α - \frac{π}{2})}$ $(sin^2(pi/2+alpha)-cos^2(alpha-pi/2))/(tg^2(pi/2+alpha)-ctg^2(alpha-pi/2))$

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Simplify the expression:? (sin^2(pi/2+alpha)-cos^2(alpha-pi/2))/(tg^2(pi/2+alpha)-ctg^2(alpha-pi/2))sin2(π2+α)−cos2(α−π2)tg2(π2+α)−ctg2(α−π2)(sin^2(pi/2+alpha)-cos^2(alpha-pi/2))/(tg^2(pi/2+alpha)-ctg^2(alpha-pi/2))

(sin^2(pi/2+alpha)-cos^2(alpha-pi/2))/(tg^2(pi/2+alpha)-ctg^2(alpha-pi/2))sin2(π2+α)−cos2(α−π2)tg2(π2+α)−ctg2(α−π2)(sin^2(pi/2+alpha)-cos^2(alpha-pi/2))/(tg^2(pi/2+alpha)-ctg^2(alpha-pi/2))

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Simplify the expression:? $\frac{{sin}^{2} (\frac{π}{2} + α) - {cos}^{2} (α - \frac{π}{2})}{t g^{2} (\frac{π}{2} + α) - c t g^{2} (α - \frac{π}{2})}$ $(sin^2(pi/2+alpha)-cos^2(alpha-pi/2))/(tg^2(pi/2+alpha)-ctg^2(alpha-pi/2))$

$\frac{{sin}^{2} (\frac{π}{2} + α) - {cos}^{2} (α - \frac{π}{2})}{t g^{2} (\frac{π}{2} + α) - c t g^{2} (α - \frac{π}{2})}$ $(sin^2(pi/2+alpha)-cos^2(alpha-pi/2))/(tg^2(pi/2+alpha)-ctg^2(alpha-pi/2))$