Simplify ? $\frac{{cos}^{2} a - {sin}^{2} b}{{sin}^{2} a ∙ {sin}^{2} b} - c t g^{2} a ∙ c t g^{2} b$ $(cos^2a - sin^2b)/(sin^2a • sin^2b) - ctg^2a • ctg^2b$

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Simplify ? $\frac{{cos}^{2} a - {sin}^{2} b}{{sin}^{2} a ∙ {sin}^{2} b} - c t g^{2} a ∙ c t g^{2} b$ $(cos^2a - sin^2b)/(sin^2a • sin^2b) - ctg^2a • ctg^2b$

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Answer 1 · 2018-04-05T13:20:03

$\frac{{cos}^{2} (a) - {sin}^{2} (b)}{{sin}^{2} (a) {sin}^{2} (b)} - {cot}^{2} (a) {cot}^{2} (b) = - 1$ $(cos^2(a)-sin^2(b))/(sin^2(a)sin^2(b))-cot^2(a)cot^2(b)=-1$

Explanation:

We want to simplify

$\frac{{cos}^{2} (a) - {sin}^{2} (b)}{{sin}^{2} (a) {sin}^{2} (b)} - {cot}^{2} (a) {cot}^{2} (b)$ $(cos^2(a)-sin^2(b))/(sin^2(a)sin^2(b))-cot^2(a)cot^2(b)$

We will use the identity

${sin}^{2} (x) + {cos}^{2} (x) = 1$ $sin^2(x)+cos^2(x)=1$

Thus

$\frac{{cos}^{2} (a) - {sin}^{2} (b)}{{sin}^{2} (a) {sin}^{2} (b)} - {cot}^{2} (a) {cot}^{2} (b)$ $(cos^2(a)-sin^2(b))/(sin^2(a)sin^2(b))-cot^2(a)cot^2(b)$

$\frac{{cos}^{2} (a) - {sin}^{2} (b)}{{sin}^{2} (a) {sin}^{2} (b)} - \frac{{cos}^{2} (a) {cos}^{2} (b)}{{sin}^{2} (a) {sin}^{2} (b)}$ $(cos^2(a)-sin^2(b))/(sin^2(a)sin^2(b))-(cos^2(a)cos^2(b))/(sin^2(a)sin^2(b))$

$\frac{{cos}^{2} (a) - {sin}^{2} (b) - {cos}^{2} (a) {cos}^{2} (b)}{{sin}^{2} (a) {sin}^{2} (b)}$ $(cos^2(a)-sin^2(b)-cos^2(a)cos^2(b))/(sin^2(a)sin^2(b))$

$\frac{{cos}^{2} (a) (1 - {cos}^{2} (b)) - {sin}^{2} (b)}{{sin}^{2} (a) {sin}^{2} (b)}$ $(cos^2(a)(1-cos^2(b))-sin^2(b))/(sin^2(a)sin^2(b))$

$\frac{{cos}^{2} (a) {sin}^{2} (b) - {sin}^{2} (b)}{{sin}^{2} (a) {sin}^{2} (b)}$ $(cos^2(a)sin^2(b)-sin^2(b))/(sin^2(a)sin^2(b))$

$\frac{- {sin}^{2} (b) (1 - {cos}^{2} (a))}{{sin}^{2} (a) {sin}^{2} (b)}$ $(-sin^2(b)(1-cos^2(a)))/(sin^2(a)sin^2(b))$

$\frac{- {sin}^{2} (b) {sin}^{2} (a)}{{sin}^{2} (a) {sin}^{2} (b)}$ $(-sin^2(b)sin^2(a))/(sin^2(a)sin^2(b))$

$- 1$ $-1$

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Simplify ? $\frac{{cos}^{2} a - {sin}^{2} b}{{sin}^{2} a ∙ {sin}^{2} b} - c t g^{2} a ∙ c t g^{2} b$ $(cos^2a - sin^2b)/(sin^2a • sin^2b) - ctg^2a • ctg^2b$

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Simplify ? cos2a−sin2bsin2a∙sin2b−ctg2a∙ctg2b (cos^2a - sin^2b)/(sin^2a • sin^2b) - ctg^2a • ctg^2b

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Simplify ? $\frac{{cos}^{2} a - {sin}^{2} b}{{sin}^{2} a ∙ {sin}^{2} b} - c t g^{2} a ∙ c t g^{2} b$ $(cos^2a - sin^2b)/(sin^2a • sin^2b) - ctg^2a • ctg^2b$