Question

If b tanθ = a, find the values of `(cosθ + sinθ)/(cosθ - sinθ)`.

Answer 1

b tanθ = a

⇒ tanθ = `"a"/"b"`

Consider `(cosθ + sinθ)/(cosθ - sinθ)`
Dividing the numerator and demoninator by cosθ, we get

`(cosθ + sinθ)/(cosθ - sinθ)`

= `(1 + sinθ/cosθ)/(1 - sinθ/cosθ)`

= `(1 + tanθ)/(1 - tanθ)`

= `(1 + "a"/"b")/(1 - "a"/"b")`

= `(("b" + "a")/"b")/(("b" - "a")/"b")`

= `(("b" + "a"))/(("b" - "a")`.