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Question-52082




Question Number 52082 by ajfour last updated on 03/Jan/19
Commented by ajfour last updated on 03/Jan/19
Express 𝛂 in terms of 𝛉.
$${Express}\:\boldsymbol{\alpha}\:{in}\:{terms}\:{of}\:\boldsymbol{\theta}. \\ $$
Answered by mr W last updated on 03/Jan/19
4α+2β=π    ...(i)  β=2γ     ...(ii)  θ=4α+γ   ...(iii)  (i)−2(ii)+4(iii):  4α+4θ=π+16α  ⇒α=(θ/3)+(π/(12))
$$\mathrm{4}\alpha+\mathrm{2}\beta=\pi\:\:\:\:…\left({i}\right) \\ $$$$\beta=\mathrm{2}\gamma\:\:\:\:\:…\left({ii}\right) \\ $$$$\theta=\mathrm{4}\alpha+\gamma\:\:\:…\left({iii}\right) \\ $$$$\left({i}\right)−\mathrm{2}\left({ii}\right)+\mathrm{4}\left({iii}\right): \\ $$$$\mathrm{4}\alpha+\mathrm{4}\theta=\pi+\mathrm{16}\alpha \\ $$$$\Rightarrow\alpha=\frac{\theta}{\mathrm{3}}+\frac{\pi}{\mathrm{12}} \\ $$
Commented by ajfour last updated on 03/Jan/19
Thank you sir!
$${Thank}\:{you}\:{sir}! \\ $$

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