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Question
If tanθ = `1/2`, evaluate `(2sin theta + 3cos theta)/(4cos theta + 3sin theta)`
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Solution
Alternative Method :
Given: tan θ = `1/2`
∴ `(2sin theta + 3cos theta)/(4cos theta + 3sin theta) = ((2sin theta)/cos theta + 3)/(4 + (3sintheta)/cos theta)` ...[Dividing numerator and denominator by cos θ]
= `(2tan theta + 3)/(4 + 3 tan theta)`
= `(2(1/2) + 3)/(4 + 3(1/2))`
= `4/((11/2))`
= `8/11`
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