A positive acute angle is divided into two parts whose tangents are 1/2 and 1/3. Show that the angle is π/4
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Let tan a= 1/2 and tan b= 1/3
=> a = tan^-1(1/2) and b = tan^-1(1/3)
=> a+b = tan^-1 [ (1/2 + 1/3)/(1- 1/2.1/3) ]
=> a+b = tan^-1 [ (5/6) / (5/6) ]
=> a+b = tan^-1 (1)
=> x(say) = 45°
=> a = tan^-1(1/2) and b = tan^-1(1/3)
=> a+b = tan^-1 [ (1/2 + 1/3)/(1- 1/2.1/3) ]
=> a+b = tan^-1 [ (5/6) / (5/6) ]
=> a+b = tan^-1 (1)
=> x(say) = 45°
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Proved
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