Question

Tan20°tan40°tan80°=√3​

Answer 1

Answer:

Step-by-step explanation:

Tan20°tan40°tan80° = (sin 40 *sin 80) * sin 20 /(cos 40 *cos 80 ) cos 20

now, multiplying numerator and denominator by 2,

=(2*sin 40*sin 80) *sin 20 /(2 cos 40*cos 80) cos 20]

=(cos 40° - cos 120°)*sin 20°/( (cos 120+ cos 40) cos 20°

=(2 cos 40° +1) sin 20° /(2 cos 40°-1) cos 20°

=(2 cos 40*sin 20° + sin 20°) /(2 cos 40° cos 20° -cos 20°)

=(sin 60° - sin 20° +sin 20°)/ (cos 60°+sin 20°-sin 20°)

= sin 60°/cos 60°

= tan 60°

= √3.

Hence proved