What is (tan(x)-cot(x))/(tan(x)+cot(x)) ?

The solution to (tan(x)-cot(x))/(tan(x)+cot(x)) is -cos(2x)

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simplify (tan(x)-cot(x))/(tan(x)+cot(x))

simplify

\frac{tan ( x ) - cot ( x )}{tan ( x ) + cot ( x )}

- cos (2 x)

Solution steps

\frac{tan ( x ) - cot ( x )}{tan ( x ) + cot ( x )}

Simplify

tan (x) - cot (x) : - 2 cot (2 x)

= \frac{- 2 cot ( 2 x )}{tan ( x ) + cot ( x )}

Simplify

tan (x) + cot (x) : 2 csc (2 x)

= \frac{- 2 cot ( 2 x )}{2 csc ( 2 x )}

Cancel the common factor:

2

= \frac{- cot ( 2 x )}{csc ( 2 x )}

Simplify

\frac{- cot ( 2 x )}{csc ( 2 x )} : - cos (2 x)

= - cos (2 x)

8 x^{8} y^{3} z^{32}

cos^{2} (2 x) + sin^{2} (2 x)

\frac{sin ( 2 x )}{sin ( x )}

(2 x^{4} - \frac{1}{4 x ^{6}})^{8}

(448)^{3}

What is (tan(x)-cot(x))/(tan(x)+cot(x)) ?
The solution to (tan(x)-cot(x))/(tan(x)+cot(x)) is -cos(2x)