Question

Use identities to simplify

Answer 1

(B)

Explanation:

$(\sec \beta + 1)(\tan \beta \csc \beta - 1)$

$=\left(\dfrac{1}{\cos\beta} + 1 \right) \left(\dfrac{\sin \beta}{\cos \beta} \dfrac{1}{\sin \beta} - 1 \right)$

$=\left(\dfrac{1}{\cos\beta} + 1 \right) \left(\dfrac{1}{\cos \beta} - 1 \right)$

$= \left(\dfrac{1}{\cos^2 \beta} - 1 \right)$

$= \left(\dfrac{1 - \cos^2 \beta}{\cos^2 \beta} \right)$

$= \dfrac{\sin^2 \beta}{\cos^2 \beta}$

$= \tan^2 \beta$