Question

if sin(A-B) =1/2AND cos(A-B) =1/2 then find A and B

Answer 1

sin(A-B) = 1/2

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We know, 1/2 = sin30 
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sin(A -B) = sin30

( A -B) = 30    ----1equation

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Cos(A + B)= 1/2 

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We know, 1/2 = cos60
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Cos(A + B) = cos60

A + B = 60    ----2equation



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Adding both the equations,

A - B = 30 
A + B = 60 
___________
2A = 90 
_________

A = 90/2 

A = 45 


putting the value of A in 1equation,

A - B = 30 

45 - B = 30 

45 - 30 = B 

15 = B 




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A = 45 
B = 15 



i hope this will help you

(-:

Answer 2

HEY FRIEND

HERE IS YOUR ANSWER

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GIVEN :

sin(A-B) =1/2

We know that :

sin30°=1/2

So, A-B=30°----------------(i)

NOW,

cos(A+B)=1/2 (Given)

We know that :

cos60°=1/2

So, A+B=60°----------------(ii)

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NOW, ADDING EQ(i) AND EQ(ii)

A-B=30°
A+B=60°
_______

A+A-B+B=30°+60°

2A=90°

A=90°/2

A=45°

Putting value of A in eq(ii)

A+B=60

45+B=60

B=60-45

B=15

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WE GET :

A=45°

B=15°

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HOPE THIS HELPS YOU ☺