Question

$(1-\tan A)(\cot A+1)$ is equal to

• A. $(1-\tan A)(1+tanA)$
• B. $(1+\tan A)(cotA-1)$
• C. $(1+\tan A)(1-cotA)$
• D. $(\tan A-1)(\cot A-1)$

Answer 1

Answer: (B)

$(1-\tan A)(\cot A+1)$
$=\left(1-\frac{1}{\cot A}\right)\left(\frac{1}{\tan A}+1\right)$
$=\left(\frac{\cos A-1}{\cot A}\right)\left(\frac{1+\tan A}{\tan A}\right)$
$=(1+\tan A)(\cot A-1)$