簡約 (tan(x)-cot(x))/(tan(x)+cot(x))

解

簡約

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

- cos (2 x)

解答ステップ

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

簡素化

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

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

簡素化

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

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

共通因数を約分する:

2

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

簡素化

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

= - cos (2 x)