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Question
If 3 cot θ = 2, find the value of `(4sin theta - 3 cos theta)/(2 sin theta + 6cos theta)`.
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Solution
`cot theta = 2/3`
`= ((4 sin theta - 3 cos theta)/sin theta)/((2sin theta + 6 cos theta)/sin theta)`
`= (4 - 3 cot theta)/(2 + 6 cot theta)`
`= (4 - 3 xx 2/3)/(2 + 6 xx 2/3)`
`= (4 + 2)/(2 + 4) = 2/6`
`= 1/3`
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