Question

If 5 cosx + 12 cos y = 13.then the
maximum value of 5 sinx + 12 siny is​

Answer 1

Answer:

(5cosx+12cosy)=13

(5cosx+12cosy)2=132=169

25cos2x+120cosxcosy+144cos2y=169−(1)

5sinx+12siny=A

25sin2x+120sinxsiny+144siny=A2

adding eqution 1 and 2

25+144+120(cosxcosy+sinxsiny)

=A2+169

120(cosxcosy+sinxsiny)=A2

120cos(x−y)=A2

A2 is a max whencos(x−y)=1

A2max=120

Amax=120‾‾‾‾√

Step-by-step explanation:

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Answer 2

Answer:

5cosx+12cosy)=13

(5cosx+12cosy)2=132=169

25cos2x+120cosxcosy+144cos2y=169−(1)

5sinx+12siny=A

25sin2x+120sinxsiny+144siny=A2

adding eqution 1 and 2

25+144+120(cosxcosy+sinxsiny)

=A2+169

120(cosxcosy+sinxsiny)=A2

120cos(x−y)=A2

A2 is a max whencos(x−y)=1

A2max=120

Amax=120‾‾‾‾√

Step-by-step explanation:

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