Question

tan(pi/5)+2tan(2pi/5)+4cot(4pi/5) =

Answer 1

hope this helps uh...

Answer 2

•To find:-

Tan(pi/5)+2tan(2pi/5)+4cot(4pi/5) =?

•Solution:-

if tan (π/5) = tan A = √ (5 - 2√5)

tan 2π/5 = tan 2A = 2 tanA/1- tan²A = √(5-2√5)/√5 - 2

tan 4π/5 = tan 4A = 2 tan²2A/ 1- tan²2A

Cot 4A = cot 4π/5 = 2-√5 / (√5 -2)√(5-2√5) = -1/√(5-2√5)

so Tan(pi/5)+2tan(2pi/5)+4cot(4pi/5)

= √ (5 - 2√5) + 2√(5-2√5)/(√5 - 2) - 4/√(5-2√5)

= 1/√(5-2√5)