Question

Prove that tan 20 . tan 40 . tan 60 . tan80 = 3​

Answer 1

Step-by-step explanation:

sqrt 3 * sin20/cos20 * sin40/cos40 * sin80/cos80

sqrt 3 * 2(cos20 - cos60) /2(cos60 + cos20) * sin80/cos80

sqrt 3 * (cos 20 - 1/2)/(1/2 + cos20) * sin80/cos80

sqrt 3 * (2 cos20 - 1)/(1 + 2 cos20) * sin80/cos80

sqrt 3 * (sin100 + sin60 - sin10)/(cos80 + cos100 + cos60)

sqrt 3 * (sqrt 3/2 + 2 cos90 * sin10) /(1/2 + 2 cos90 * cos10)

sqrt 3 * sqrt 3/2 * 2

= 3

hence proved!