Question 151158: tan ((pi/6)+pi/4))
Answer by orca(409)   (Show Source):
You can put this solution on YOUR website! Use the formula
tan(A + B)= [tanA + tanB]/[1 - tanAtanB]
Also note that
tan(pi/6)= 1/sqrt(3)
tan(pi/4)= 1
tan ((pi/6)+(pi/4))
=[tan(pi/6)+tan(pi/4)]/[1-tan(pi/6)tan(pi/4)]
=[1/sqrt(3)+1]/[1-1/sqrt(3)]
=[1+sqrt(3)]/[sqrt(3)-1]
={[1+sqrt(3)][sqrt(3)+1]}/{[sqrt(3)-1][sqrt(3)+1]}
={[sqrt(3)+1][sqrt(3)+1]}/{[sqrt(3)-1][sqrt(3)+1]}
=[sqrt(3)+1]^2/{[sqrt(3)-1][sqrt(3)+1]}
=[3+2sqrt(3)+1]/(3-1)
=[4 + 2sqrt(3)]/2
= 2 + sqrt(3)
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