Question

Reduce: (Secθ - Cosθ)Cotθ

Answer 1

Respuesta:

$\text{sen}\theta$

Explicación paso a paso:

$\left(\text{sec}\theta-\cos\theta\right)\cot\theta\\=\left(\cfrac{1}{\cos\theta}-\cos\theta\right)\left(\cfrac{\cos\theta}{\text{sen}\theta}\right)\\=\left(\cfrac{1-\cos^{2}\theta}{\cos\theta}\right)\left(\cfrac{\cos\theta}{\text{sen}\theta}\right)\\=\left(\cfrac{\text{sen}^{2}\theta}{\cos\theta}\right)\left(\cfrac{\cos\theta}{\text{sen}\theta}\right)\\\\\\=\cfrac{\text{sen}^{2}\theta\cos\theta}{\text{sen}\theta\cos\theta}\\\\=\text{sen}\theta$