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Question

Given 3sinβ+5cosβ=5, then the value of (3cosβ5sinβ)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 A 9
3sinβ+5cosβ=5
5cosβ=53sinβ
Squaring both the sides we get
25cos2β=25+9sin2β30sinβ
30sinβ=34sin2β
Therefore
3034=sinβ ...(i)
Hence cosβ=1sin2β=1634 ...(ii)
Substituting in the expression the values of sinβ and cosβ
Therefore
(3cosβ5sinβ)2
=((3)1634(5)3034)2
=(4815034)2
=(10234)2
=(3)2
=9
Hence the answer is A

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