What is [ 1/(1-sin^2(A))]-[tan(A) 1/(cot(A))] ?

The solution to [ 1/(1-sin^2(A))]-[tan(A) 1/(cot(A))] is 1

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simplify [ 1/(1-sin^2(A))]-[tan(A) 1/(cot(A))]

simplify

[\frac{1}{1 - sin ^{2} ( A )}] - [tan (A) \frac{1}{cot ( A )}]

1

Solution steps

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

Simplify

(\frac{1}{1 - sin ^{2} ( A )}) - (tan (A) \frac{1}{cot ( A )}) : \frac{1}{1 - sin ^{2} ( A )} - tan (A) \frac{1}{cot ( A )}

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

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

tan (A) \frac{1}{cot ( A )} = \frac{tan ( A )}{cot ( A )}

= \frac{1}{cos ^{2} ( A )} - \frac{tan ( A )}{cot ( A )}

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

\frac{tan ( A )}{cot ( A )} = tan^{2} (A)

= sec^{2} (A) - tan^{2} (A)

Use the Pythagorean identity:

sec^{2} (x) = tan^{2} (x) + 1

sec^{2} (x) - tan^{2} (x) = 1

= 1

(ln (5))^{2}

\frac{\frac{3}{12} + \frac{7}{8} ( \frac{3}{4} + \frac{2}{3} )}{( - \frac{1}{3} ) ^{3}}

- 4 x - 3

(6 x^{2} + 3 y^{2} - 7 x + 4 y - 2) - (2 x^{2} - y^{2} - 7 x + 8)

\frac{( 4 h ^{4} ) ^{4}}{4 h ^{- 8}}

What is [ 1/(1-sin^2(A))]-[tan(A) 1/(cot(A))] ?
The solution to [ 1/(1-sin^2(A))]-[tan(A) 1/(cot(A))] is 1