Question

How do we find `tan120^@` using double angle identity?

Answer 1

`tan120^o=-sqrt3`

Explanation:

We use the double angle identity `tanA=(2tanA)/(1-tan^2A)`.

As such `tan120^o=tan(2xx60^o)`

Hence, `tan120^o=(2xxtan60^o)/(1-tan^(2)60^o)`

= `(2xxsqrt3)/(1-(sqrt3)^2)`

= `(2sqrt3)/(1-3)=(2sqrt3)/(-2)=-sqrt3`