Question

Prove That:-
tan(π/12) * tan(5π/12) * tan(7π/12) * tan(11π/12) = 1

Answer 1

\[\tan(\frac{11 \pi}{12}) = \tan(\pi - \frac{ \pi}{12}) = -\tan(\frac{\pi}{12})\]

Answer 2

\[\tan(\frac{7 \pi}{12}) = \tan(\pi - \frac{ 5 \pi}{12}) = -\tan(\frac{5 \pi}{12})\]

Answer 3

yeah, i've understood dat portion...but could you plz solve the whole problem...i mean i'm nt getting it completely

Answer 4

Where are you not getting it?

Answer 5

\[LHS: [\tan(\frac{\pi}{12})\tan(\frac{5 \pi}{12})]^2\]

Answer 6

yeah, then? how come the answer is 1?

Answer 7

\[\tan(\frac{5 \pi}{12}) = \tan(\frac{\pi}{2} - \frac{\pi}{12}) = \cot(\frac{\pi}{12})\]

Answer 8

ooooooooo yeah, i got it :P

Answer 9

\[LHS: [\tan(\frac{\pi}{12})\cot(\frac{ \pi}{12})]^2\]

Answer 10

Rest you know..

Answer 11

thank you, very much! :)

Answer 12

You are welcome dear.. :)