Question

sin(A-B) =1/2 ,cos (A+B )= 1/2 then find the value of A and B​

Answer 1

Question :

• If sin(A-B) =1/2, cos (A+B )= 1/2 then find the value of A and B.

Answer

Given:-

• sin(A-B) =1/2
• cos (A+B )= 1/2

To find :-

• The value of A and B.

Solution :-

$\bf \:Consider \: sin(A - B) = \dfrac{1}{2}$

$\bf\implies \:sin(A - B) = sin30°$

On comparing, we get

$\bf\implies \:A - B = 30°....(1)$

$\bf \:Consider \: cos(A + B) = \dfrac{1}{2}$

$\bf\implies \:cos(A + B) = cos60°$

On comparing, we get

$\bf\implies \:A + B = 60°.......(2)$

Adding equations (1) and (2), we get

$\bf\implies \:A + B + A - B = 60° + 30°$

$\bf\implies \:2A = 90°$

$\bf\implies \:A = 45°$

Put A = 45 in equation (2) we get,

$\bf\implies \:45° + B = 60°$

$\bf\implies \:B = 15°$

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