Given 3sinβ+5cosβ=5, then the value of (3cosβ−5sinβ)2 is
A
9
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B
95
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C
13
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D
19
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Solution
The correct option is A9 3sinβ+5cosβ=5 5cosβ=5−3sinβ Squaring both the sides we get 25cos2β=25+9sin2β−30sinβ 30sinβ=34sin2β Therefore 3034=sinβ ...(i) Hence cosβ=√1−sin2β=1634 ...(ii) Substituting in the expression the values of sinβ and cosβ Therefore (3cosβ−5sinβ)2 =((3)1634−(5)3034)2 =(48−15034)2 =(−10234)2 =(−3)2 =9 Hence the answer is A