Given that, cos (A + B) = 12 ⇒ cos (A+B) = cos 45° As cos 45° = 12 ⇒ A+B=45° . . . . . . . . . . . (i) And, cos (A-B) = 32 ⇒cos (A-B) = cos 30° As cos 30° = 32 ⇒ A-B=30° . . . . . . . .(ii) Adding, equation (i) and (ii) we get A + B = 45° A - B=30°2A = 75° ⇒ A = 75°2 = 37.5° Now, we put A = 37.5° in equation (i) A+B=45° ⇒ 37.5° + B = 45° ∴ B=45° -37.5° = 7.5° ∴ A=37.5° and B = 7.5° (answer)
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