Question 151396
tan(A−B) = (tan A − tan B) / (1 + tan A tan B)


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tan(5pi/3 - pi/4) = (tan(5pi/3) - tan(pi/4)) / (1 + (tan(5pi/3)(tan(pi/4))

= (tan(-pi/3) - 1) / (1 + (tan(-pi/3)*1)

= (-sqrt(3)-1) / (1 + (-sqrt(3)*1)

= -(1+sqrt(3))/(1 - sqrt(3))

= [-(1+sqrt(3))^2]/ (-2)

= 3.7321...
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Cheers,
Stan H.