Question

tan 20 = k then tan 250 + tan 340/tan 200 - tan 110 = ​

Answer 1

Answer:

$\frac{ 1-k^{2}}{1+k^{2}}$

Step-by-step explanation:

tan 20°= k         (1) [given]

tan 250°= tan (270°-20°) = cot 20° = 1/tan 20° = 1/k

tan 340°= tan(360°-20°) = - tan 20° = -k

tan 200°= tan (180°+20°) = tan 20° =k

tan 110°= tan (90°+20°) = -cot 20° = -1/tan 20° = -1/k

⇒(tan 250°+tan 340°)/( tan  200° -tan 110°)

= (1/k -k)/(k + 1/k)

= (1 -k²)/ (1+k²)