If tan (A+B) = x and tan B =1/2, prove that tan A = (2x-1)/(x+2) and obtain an expression for tan (A-B) in terms of x. If tan (A-B)=1/3 and A is acute, find A without using tables.

tanA+B=x=tanA+tanB1-tanAtanBx=tanA+121-tanA2x-xtanA2=tanA+12x-12=tanA+xtanA2=tanA1+x22x-12=tanAx+22So tanA=2x-1x+2tanA-B=tanA-tanB1+tanAtanB=2x-1x+2-121+12×2x-1x+2Now simplify this for your own practice to get the result.

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