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