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If \( \sin (A+B)=\frac{1}{2} \) and \( \cos (A+B)=\frac{1}{2}, 0^{\circ}B \) then values of \( A \) and \( B \) are |
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Answer» \(sin(A - B) = \frac 12 = sin 30°\) ⇒ A - B = 30° ....(i) \(cos(A + B) = \frac 12 = 60°\) ⇒ \(A + B = 60° \) .....(ii) On adding equations (i) & (ii), we get \((A - B) + (A + B) = 30° + 60° = 90°\) ⇒ \(2A = 90°\) ⇒ \(A = \frac{90°}2 = 45° \) \(\therefore A + B = 60°\) ⇒ \(B = 60° - A = 60° - 45° = 15°\) |
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