First slide

Compound angles

Question

If $\tan (A + B) = p, \tan (A - B) = q$ then $\cot 2 B =$

Moderate

A

$\frac{1 + p q}{p - q}$
B

$\frac{1 + p q}{p + q}$
C

$\frac{1 - p q}{p - q}$
D

$\frac{1 - p q}{p + q}$

Solution

2B=(A+B)-(A-B) Apply cot on both sides
cot2B= $\frac{c o t (A + B) c o t (A - B) + 1}{c o t (A - B) - c o t (A + B)}$
$= \frac{\frac{1}{p} \frac{1}{q} + 1}{\frac{1}{q} - \frac{1}{q}} = \frac{1 + p q}{p - q}$

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