Question

The value of `tan 40^circ + tan 20^circ + sqrt(3) tan 20^circ tan 40^circ` is ______.

विकल्प

• `sqrt(12)`

• `1/sqrt(3)`

• `sqrt(3)`

• `sqrt(3)/2`

Answer 1

The value of `tan 40^circ + tan 20^circ + sqrt(3) tan 20^circ tan 40^circ` is `underlinebb(sqrt(3))`.

Explanation:

∵ tan 60° = tan (40° + 20°)

`\implies sqrt(3) = (tan 40^circ +  tan 20^circ)/(1 - tan 40^circ  tan 20^circ)`

`\implies sqrt(3) - sqrt(3)  tan 40^circ  tan 20^circ` = tan 40° + tan 20°

∴  `tan 40^circ +  tan 20^circ + sqrt(3)  tan 40^circ  tan 20^circ = sqrt(3)`