First slide

Compound angles

Question

If $\tan A - \tan B = x and \cot B - \cot A = y,$ then the value of $\cot (A - B)$ is

Moderate

A

$\frac{x - y}{x y}$
B

$\frac{1}{x^{2}} + \frac{1}{y^{2}}$
C

$\frac{x + y}{x y}$
D

$x y$

Solution

$\cot (A - B) = \frac{\cot A \cot B + 1}{\cot B - \cot A} = \frac{\frac{y}{x} + 1}{y} = \frac{x + y}{x y}$

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