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Question
If 3 tan θ = 4, find the value of `(4cos theta - sin theta)/(2cos theta + sin theta)`
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Solution
3 tan theta = 4 find `(4cos theta - sin theta)/(2cos theta + sin theta)` ....(i)
`tan theta = 4/3`
Dividing equation (i) with cos θ we get
`= ((4cos theta - sin theta)/cos theta)/((2 cos theta + sin theta)/cos theta) = (4 - tan theta)/(2 + tan theta) [∵ sin theta/cos theta = tan theta]`
`= (4 - tan theta)/(2 + tan theta) [∵ sin theta/cos theta = tan theta]`
`= (4 - 4/1)/(2 + 4/5)`
`= (12 - 4)/(6 + 4)`
`= 8/10`
`= 4/5`
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