Question

if tan 20 = α
then tan 250 + tan 340 whole divided by tan 200 - tan 110 =

Answer 1

$tan 340 = tan (360-20)=-tan 20 = - \alpha\\\\tan250=-tan(90-340)=-cot340 =1/ \alpha \\\\tan200 = tan(180+20)= tan20 =\alpha\\\\tan110=tan(90+20)=-cot20=-1/ \alpha$

$LHS = \frac{1/ \alpha - \alpha }{ \alpha +1/ \alpha }=\frac{1- \alpha^2 }{1+ \alpha^2 }$

Answer 2

if tan 20 = a then cot 20 = 1/a

tan 250 + tan 340 = tan (270-20) + tan (360-20)
=>cot 20 - tan20
=>1/a - a
=>[1-(a^2)]/a........eqn1

tan 200 + tan 110 = tan (180+20) + tan (90+20)
=>tan 20 - cot 20
=>a - 1/a
=>[(a^2)-1]/a .........eqn2

eqn1/eqn2
=>{[1-(a^2)]/a} / {[(a^2)-1]/a}
=>[1-(a^2)] / [(a^2)-1]
=>-1