What is ((cot(A)+csc(A))(cot(A)-csc(A)))/((1-cos(A))(1+cos(A))) ?

The solution to ((cot(A)+csc(A))(cot(A)-csc(A)))/((1-cos(A))(1+cos(A))) is -csc^2(A)

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simplify ((cot(A)+csc(A))(cot(A)-csc(A)))/((1-cos(A))(1+cos(A)))

simplify

\frac{( cot ( A ) + csc ( A ) ) ( cot ( A ) - csc ( A ) )}{( 1 - cos ( A ) ) ( 1 + cos ( A ) )}

- csc^{2} (A)

Solution steps

\frac{( cot ( A ) + csc ( A ) ) ( cot ( A ) - csc ( A ) )}{( 1 - cos ( A ) ) ( 1 + cos ( A ) )}

Simplify

(cot (A) + csc (A)) (cot (A) - csc (A)) : - 1

= \frac{- 1}{( 1 - cos ( A ) ) ( 1 + cos ( A ) )}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{1}{( 1 - cos ( A ) ) ( 1 + cos ( A ) )}

(1 + cos (A)) (1 - cos (A)) = sin^{2} (A)

= - \frac{1}{sin ^{2} ( A )}

Simplify

\frac{1}{sin ^{2} ( A )} : csc^{2} (A)

= - csc^{2} (A)

\frac{2}{( s ^{2} + 1 ) ( s ^{2} + 4 )}

12 (8 + π)

sin (x) (cot (x) - csc (x)) + 1

\frac{20}{( s ^{2} + 6 s + 25 ) ( s + 1 )}

What is ((cot(A)+csc(A))(cot(A)-csc(A)))/((1-cos(A))(1+cos(A))) ?
The solution to ((cot(A)+csc(A))(cot(A)-csc(A)))/((1-cos(A))(1+cos(A))) is -csc^2(A)