Given that \tan \frac x2=\frac{1-\cos(x)}{sin(x)}, deduce that \tan \frac{\pi}{12}=2−\sqrt3

pozicijombx 2022-01-25 Answered
Given that tanx2=1cos(x)sin(x), deduce that tanπ12=23
I know tanx2=1cos(x)sin(x) is true and I can prove it by squaring and taking a square root of the right side then I multiply by 0.50.5. And I will use
cosx2=1+cosx2
and
sinx2=1cosx2
But I do not understand the part of deducing.
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Expert Answer

Madelyn Townsend
Answered 2022-01-26 Author has 13 answers
I suspect this is what you need to solve:
Show that tan(112π)=23, given that
tan(x2)=1cosxsinx
This can be shown quite easily as cos(16π)=123 and sin(16π)=12. (These are well known values and I suspect you do not need to proof this.)
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