How do you simplify $(tan 5π/12 + tan (π/4))/(1 - tan (5π/12) tan (π/4))$ ?

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Answer 1 · 2015-12-02T04:01:09

Simplify trig expression

Ans: $tan (pi/3)$

Apply the trig identity: $tan (a + b) = (tan a + tan b)/(1 - tan a.tan b).$

$(tan ((5pi)/12) + tan (pi/4))/(1 - tan ((5pi)/12). tan (pi/4) =$
$= tan (pi/12 + (pi)/4) = tan ((4pi)/12) = tan (pi/3)$

How do you simplify (tan 5π/12 + tan (π/4))/(1 - tan (5π/12) tan (π/4))(tan 5π/12 + tan (π/4))/(1 - tan (5π/12) tan (π/4))?