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Question
If 4 tanθ = 3, then `((4 sintheta - costheta)/(4sintheta + costheta))` is equal to ______.
Options
`2/3`
`1/3`
`1/2`
`3/4`
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Solution
If 4 tanθ = 3, then `((4 sintheta - costheta)/(4sintheta + costheta))` is equal to `underlinebb(1/2)`.
Explanation:
Given,
4 tanθ = 3
⇒ tanθ = `3/4` ...(i)
∴ `(4 sin theta - cos theta)/(4 sin theta + cos theta) = (4 sin theta/cos theta - 1)/(4 sin theta/cos theta + 1)` ...[Divide by cos θ in both numerator and denominator]
= `(4 tan theta - 1)/(4 tan theta + 1)` ...`[∵ tan theta = sin theta/cos theta]`
= `(4(3/4) - 1)/(4(3/4) + 1)` ...[Put the value from equation (i)]
= `(3 - 1)/(3 + 1)`
= `2/4`
= `1/2`
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