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If `5cosx+12cosy=13`, then the maximum value of `5sinx+12siny` is (A) `12` (B) `sqrt(120)` (C) `sqrt(20)` (D) 13 |
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Answer» `(5cosx+12cosy)=13` `(5cosx+12cosy)^2=13^2=169` `25cos^2x+120cosxcosy+144cos^2y=169-(1)` `5sinx+12siny=A` `25sin^2x+120sinxsiny+144sin^y=A^2` adding eqution 1 and 2 25+144+120(cosxcosy+sinxsiny) `=A^2+169` `120(cosxcosy+sinxsiny)=A^2` `120cos(x-y)=A^2` `A^2` is a max when`cos(x-y)=1` `A_(max)^2=120` `A_(max)=sqrt120` |
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