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Question Number 168664 by cortano1 last updated on 15/Apr/22

$$\{\begin{array}{l}8\cos x-8\sin x=3\\ 55\tan x+\frac{55}{\tan x}=?\end{array}$$

Answered by greogoury55 last updated on 15/Apr/22

$${(8\cos x-8\sin x)}^2=9$$$$64-64\sin 2x=9$$$$\Rightarrow 55=64\sin 2x$$$$\Rightarrow \sin 2x=\frac{55}{64}$$$$\Rightarrow 55(\frac{\sin x}{\cos x}+\frac{\cos x}{\sin x})=$$$$\Rightarrow 55\left(\frac{2}{\sin 2x}\right)=\frac{55\times 2}{\left(\frac{55}{64}\right)}=128$$

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