Question

4)
if tan A - tan B=x&cot B - cot A = ythen cot(A - B) = .​

Answer 1

Step-by-step explanation:

$\tan( \alpha ) - \tan( \beta ) = x \\ \\ \\ \cos( \beta ) - \cot( \alpha ) = y \\ \\ \frac{1}{ \tan( \beta ) } - \frac{1}{ \tan( \alpha ) } = y \\ \\ \frac{ \tan( \alpha ) - \tan( \beta ) }{ \tan( \alpha ) \tan( \beta ) } = y \\ \\ \cot( \alpha ) \cot( \beta ) = \frac{y}{x} \\ \\ \cot(( \alpha - \beta )) = \frac{1}{ \tan( \alpha - \beta ) } = \frac{1 + \tan( \alpha ) \tan( \beta ) }{ \tan( \alpha ) - \tan( \beta ) } \\ \\ = \frac{ 1 + \frac{x}{y} }{x} \\ \\ = \frac{x + y}{xy}$