If-tan-tan2-tan3-find-the-exhaustive-set-of-values-of-satisfying-the-given-equation-

Question Number 14268 by Tinkutara last updated on 30/May/17

If \tan θ + \tan 2 θ = \tan 3 θ, find the

exhaustive set of values of θ satisfying

the given equation .

Answered by linkelly0615 last updated on 30/May/17

∵ t a n 3 θ = \frac{t a n θ + t a n 2 θ}{1 - t a n θ t a n 2 θ} = t a n θ + t a n 2 θ

∴ 1 - t a n θ t a n 2 θ = 1

∴ t a n θ t a n 2 θ = 0, a n d θ \notin (n + 1 / 2) π, n \in Z

You can't use 'macro parameter character #' in math mode

Commented by Tinkutara last updated on 30/May/17

What will be the complete set of

solution ?

Commented by prakash jain last updated on 30/May/17

a n o t h e r p o s s i b i l i t y i s

\tan θ + \tan 2 θ = 0