Prove that .
Hence or otherwise, find the values of between and which satisfies the equation . where is not equals to zero
The calculations I showed prove that both sides are equal, Punch.
If
Then must equal
The remaining calculations examine whether or not this is true,
but i know what you mean.
Using the double-angle formulae for CosA and SinA
Hi Punch,
if you get stuck at any of the steps 1 to 7, let me know.
The evaluation of the left fraction is
This is "tangent of the half-angle",
therefore we may express the and from the left using "half-angle formulae".
The "double angle formulae" for and are
(1)
If we replace with , we will have the "half-angle" formulae.
Therefore the half-angle formulae for and are
(2)
Then, we can write the ratio on the left in terms of
(3)
Writing 1 as
(4)
gives (5)
(6)
(7)