What is (2(1+cos^2(A)))/((1+cos(A))(1-cos(A))) ?

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

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simplify (2(1+cos^2(A)))/((1+cos(A))(1-cos(A)))

simplify

\frac{2 ( 1 + cos ^{2} ( A ) )}{( 1 + cos ( A ) ) ( 1 - cos ( A ) )}

2 csc^{2} (A) (cos^{2} (A) + 1)

Solution steps

\frac{2 ( 1 + cos ^{2} ( A ) )}{( 1 + cos ( A ) ) ( 1 - cos ( A ) )}

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

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

Use the basic trigonometric identity:

\frac{1}{sin ( x )} = csc (x)

= 2 csc^{2} (A) (cos^{2} (A) + 1)

\frac{x ^{4}}{( x ^{2} - x + 1 ) ( x ^{2} + 7 ) ^{2}}

2 x y d x + (x^{2} + 3 y^{2}) d y

(x - 1 - 2) (2 + x - 3)

\frac{( A x + B )}{( ( x - 3 ) ( x + 2 ) )}

\frac{2}{x ( 1 - x ) ( 1 + x )}

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