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