Question 944081
Please help me solve this problem:
What is the exact value of tan[(pi/6) + (pi/4)]?
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{{{tan(x+y)=(tanx+tany)/(1-tanxtany)}}}
{{{tan(pi/6+pi/4)
=(tan(pi/6)+tan(pi/4))/(1-tan(pi/6)*tan(pi/4))
=(sqrt(3)/3+1)/(1-sqrt(3)/3*(1))
=(3+sqrt(3))/(3-sqrt(3))}}}
..
Check:
tan(π/6+π/4)=tan(30+45)=tan(75)≈3.732..
exact value as computed={{{(3+sqrt(3))/(3-sqrt(3))}}}≈3.732..