Trig question and its limit (1 Viewer)

Mahan1 · Feb 19, 2017

This is the question:
let
$P = (1-tan^{2}\frac{a}{2})(1-tan^{2}\frac{a}{2^{2}}) (1-tan^{2}\frac{a}{2^{3}})...(1-tan^{2}\frac{a}{2^{m}})$
and by simplifying P, find

$lim_{m\to\infty}P$

Mahan1 · Feb 26, 2017

The way I solved it uses the identity:

$tan2x = \frac{2tanx}{1-tan^{2}x} \textrm{or} \ 1-tan^{2}x = \frac{2tanx}{tan2x}$

and simplifies the question to:

$P_{m} = cota \ 2^{m}\ tan(\frac{a}{2^{m}})$

then:

$lim_{m\to\infty}P_{m} = a \ cota$

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Trig question and its limit (1 Viewer)

Mahan1

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Mahan1

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