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Question Number 140767 by EDWIN88 last updated on 12/May/21

$$\mathrm{Solve}\mathrm{for}\mathrm{x}:2\cot {}^2\mathrm{x}+\csc {}^2\mathrm{x}-2=0$$

Answered by Ar Brandon last updated on 12/May/21

$${2\cot }^2\mathrm{x}+{\csc }^2\mathrm{x}-2=0$$$${2\cot }^2\mathrm{x}+{\cot }^2\mathrm{x}+1-2=0$$$${3\cot }^2\mathrm{x}-1=0$$$$\mathrm{cotx}=\pm \frac{\sqrt{3}}{3}\Rightarrow \mathrm{tanx}=\pm \sqrt{3}$$$$\mathrm{x}=\pm \frac{\pi }{3}+\pi \mathrm{n},\mathrm{n}\in \mathbb{Z}$$

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