Question

Show that:-
tan 60(tan 170 - tan 140)= 1+tan 170.tan140

Answer 1

sqrt(3) tan(170°)-sqrt(3) tan(140°) = tan(140°) tan(170°)+1

Answer 2

That is one way to change it around a bit.

Answer 3

\[\tan(60)(\tan170-\tan140)*\frac{1+\tan(170)\tan(140)}{1+\tan(170)\tan(140)}\]
\[\tan(60)\tan(170-140)(1+\tan(170)\tan(140))\]
\[\tan(60)\tan(30)(1+\tan(170)\tan(140))\]
\[(\sqrt{3})(\frac{1}{\sqrt{3}})(1+\tan(170)\tan(140)) = 1+\tan(170)\tan(140)\]

Answer 4

using the fact that:
\[\tan(A-B) = \frac{\tan(A)-\tan(B)}{1+\tan(A)\tan(B)}\]