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Question
If A lies in the second quadrant and 3tanA + 4 = 0, then the value of 2cotA – 5cosA + sinA is equal to ______.
Options
`(-53)/10`
`23/10`
`37/10`
`7/10`
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Solution
If A lies in the second quadrant and 3tanA + 4 = 0, then the value of 2cotA – 5cosA + sinA is equal to `23/10`.
Explanation:
Given that: 3tanA + 4 = 0
A lies in the second quadrant
tanA = `(-4)/3`
cosA = `(-3)/5` .......[A lies in second quadrant]
And sinA = `4/5` and cotA = `(-3)/4`
∴ 2cotA – 5cosA + sinA = `2((-3)/4) -5((-3)/5) + 4/5`
= `(-3)/2 + 3 + 4/5`
= `(-15 + 30 + 8)/10`
= `23/10`
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