Question

if tan 0=a/b then the value of a sin 0 + b cos 0/a sin 0-b cos 0 is

Answer 1

AnswEr :

Given that,

$\sf \: tan( \alpha ) = \dfrac{a}{b}$

To finD :

$\sf \: \dfrac{a sin( \alpha ) + b cos( \alpha ) }{a sin( \alpha ) - b cos( \alpha ) }$

Since,

sin∅/cos∅ = tan∅

Dividing the Numerator and Denominator by cos(alpha)

$\longrightarrow \: \sf \: \dfrac{a \: tan( \alpha ) + b}{a tan( \alpha ) - b} \\ \\ \longrightarrow \sf \dfrac{a \times \dfrac{a}{b} + b}{a \times \dfrac{a}{b} - b} \\ \\ \longrightarrow \: \sf \: \dfrac{ \dfrac{ {a}^{2} + {b}^{2} }{b} }{ \dfrac{ {a}^{2} - {b}^{2} }{b} } \\ \\ \longrightarrow \boxed{ \sf \: \dfrac{ {a}^{2} + {b}^{2} }{ {a}^{2} - {b}^{2} } }$