tan (π/5)+2 tan (2 π/5)+4 cot (4 π/5) is equal to

Question

tan (π/5)+2 tan (2 π/5)+4 cot (4 π/5) is equal to (A)  cot (π/5) (B)  cot (2 π/5) (C)  cot (3 π/5) (D)  cot (4 π/5)

Tardigrade Admin · Accepted Answer

Given that, tan (π/5)+2 tan (2 π/5)+4 cot (4 π/5) = tan (π/5)+2[2 cot (4 π/5)+ tan (2 π/5)] = tan (π/5)+2 cot (2 π/5) [∵ 2 cot 2 A+ tan A ] = tan (π/5)+ cot (π/5)- tan (π/5)= cot (π/5)

Q. $tan \frac{π}{5} + 2 tan \frac{2 π}{5} + 4 cot \frac{4 π}{5}$ is equal to

$cot \frac{π}{5}$

$cot \frac{2 π}{5}$

$cot \frac{3 π}{5}$

$cot \frac{4 π}{5}$

Given that,
$tan \frac{π}{5} + 2 tan \frac{2 π}{5} + 4 cot \frac{4 π}{5}$
$= tan \frac{π}{5} + 2 [2 cot \frac{4 π}{5} + tan \frac{2 π}{5}]$
$= tan \frac{π}{5} + 2 cot \frac{2 π}{5}$
$[∵ 2 cot 2 A + tan A]$
$= tan \frac{π}{5} + cot \frac{π}{5} - tan \frac{π}{5} = cot \frac{π}{5}$

Q. tan5π​+2tan52π​+4cot54π​ is equal to

cot5π​

cot52π​

cot53π​

cot54π​