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Question
Given : 5 cos A - 12 sin A = 0; evaluate:
`(sin "A"+cos"A")/(2 cos"A"– sin"A")`
Solution
5 cos A – 12 sin A = 0
5 cos A = 12 sin A
`sin "A"/cos "A" = (5)/(12)`
tan A = `(5)/(12)`
Now,
`(sin "A"+cos"A")/(2 cos"A"– sin"A") = (sin"A"/cos"A" + cos"A"/cos"A")/(2 cos"A"/cos"A" – sin"A"/cos"A")`
= `(tan "A"+1)/(2– tan "A")`
= `(5/12+1)/(2–5/12)`
= `(17/12)/(19/12)`
= `(17)/(19)`
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