If and then find the measures of angles A and B.

Question

If $2 \sin (A + B) = \sqrt{3}$ and $\cos (A - B) = 1,$ then find the measures of angles A and B. $0 \leq A, B, (A + B) \leq 90 ° .$

Smart Achievers · Accepted Answer

$(30^{o})$

$2 \sin (A + B) = \sqrt{3} \Rightarrow \sin (A + B) = \frac{\sqrt{3}}{2} = \sin 60 °$

$\Rightarrow A + B = 60 °$ ....(i)

$\cos (A - B) = 1 = \cos 0 °$

$\Rightarrow A - B = 0 °$ ....(ii)

Adding (i) and (ii), we get $A = B = 30 °$

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