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Ask iit jee aieee pet cbse icse state board community Community Discussion Question: find the value
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ashish_banga (937)

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if SinA + sinB = 1/2   and CosB + CosA = 31/2 / 2  


 


find the value of 3A + B

    
allamraju (3410)

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Is there any relation between A,B,C like they are the angles of a triangle etc

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ashish_banga (937)

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sorry everyone. i have edited the question
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joyfrancis (1504)

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Just by observation it is clear that A=pi/2 and B=-pi/6 would satisfy both conditions.


Hence 3A + B = 3pi/2 - pi/6 = 4pi/3 


 


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allamraju (3410)

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sinA+sinB=2sin(A+B/2)cos(A-B/2) and cosA+cosB=2cos(A+B/2)cos(A-B/2)

dividing 1 by 2,we have,tan(A+B/2)=1/rt3A+B=pi/3.

Substituting in 1,sinA+sin(pi/3-A)=1/22sin(pi/6)cos(A-pi/6)=1/2A=pi/6+pi/3=pi/2B=-pi/6.

Hence,3A+B=4pi/3

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