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Question
If 5 tan θ = 4, find the value of `(5 sin θ + 3 cos θ)/(5 sin θ + 2 cos θ)`
Solution
5 tan θ = 4
tan θ = `4/5`
`sin θ/cos θ = 4/5`
`(5sin θ + 3cos θ)/(5sin θ + 2cos θ) = ((5sin θ)/(cos θ) + 3(cos θ)/(cos θ))/((5sin θ)/(cos θ) + (2cos θ)/(cos θ))` ....[Nr., and Dr. dividing by cos θ]
` = (5 xx 4/5 + 3)/(5 xx 4/5 + 2)`
` = (4 + 3)/(4 + 2) = 7/6`
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