Question

If tan A `=a/b`, then find the value of `("a sin A- b cos A")/("a sin A + b cos A")`.

Answer 1

tan A = `a/b`
Now `("a sinA-b cosA")/("a sin A+bcosA")=((a sinA)/(cosA)-b)/((a sinA)/(cosA)+b)`
(Divide `N^( r)` and `D^(r )` by cos A)
`=("a tanA-b")/("a tan A+b")= (a.a/b-b)/(a.a/b+b)`
`=((a^(2)-b^(2))/b)/((a^(2)+b^(2))/b)= (a^(2)-b^(2))/(a^(2)+b^(2))`. Ans