jika tan A + tan B=a dan cotan A + cotan B=b,nilai dari cotan (A+B) =...

Materi : Trigonometri 
Kelas : XI SMA 
Kata Kunci : Tangen dan Cotangen

Diketahui :
Tan A + Tan B = α
Cotan A + Cotan B = β

Ditanya : 
Cotan (A + B) = ... ?

Dijawab :
[tex]\text{Cotan A + Cotan B =} \,\ \beta\\\frac{1}{\text{Tan A}} + \frac{1}{\text{Tan B}} = \beta \\\frac{\text{Tan A + Tan B}}{\text{Tan A . Tan B}} = \beta\\\text{Tan A . Tan B} = \frac{ \alpha }{ \beta } [/tex]

[tex]\text{Cotan (A + B)}\\= \frac{1}{\text{Tan (A + B)}}\\= \frac{1}{\frac{\text{Tan A + Tan B}}{\text{1 - Tan A . Tan B}}}\\= \frac{\text{1 - Tan A . Tan B}}{\text{Tan A + Tan B}}\\ = \frac{1 - \frac{ \alpha }{ \beta } }{ \alpha }\\ = \frac{ \frac{ \beta - \alpha }{ \beta } }{ \alpha }\\ = \frac{ \beta - \alpha }{ \alpha \beta } [/tex]