Question

If 12 sin θ = 35 cos θ, find `(sin θ − cos θ)/(sin θ + cos θ)`

Answer 1

Given:

12 sin θ = 35 cos θ

Step 1: Find tan⁡ θ

tan⁡ θ = `sin θ/cosθ = 35/12`

Step 2: Required expression 

`(sin θ − cos θ​)/(sin θ + cos θ )`

Divide numerator and denominator by cos ⁡θ:

= `(sin θ/cos θ − 1)/(sin θ/cos θ + 1)`

= `(tan θ − 1)/(tan θ + 1)`

Step 3: Substitute tan ⁡θ = `35/12`

= `(35/12 − 1)/(35/12 + 1)`

= `(23/12)/(47/12)`

= `23/47`