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Solve-for-x-2cot-2-x-csc-2-x-2-0-




Question Number 140767 by EDWIN88 last updated on 12/May/21
Solve for x : 2cot^2 x + csc^2 x−2 = 0
$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}\::\:\mathrm{2cot}\:^{\mathrm{2}} \mathrm{x}\:+\:\mathrm{csc}\:^{\mathrm{2}} \mathrm{x}−\mathrm{2}\:=\:\mathrm{0}\: \\ $$
Answered by Ar Brandon last updated on 12/May/21
2cot^2 x+csc^2 x−2=0  2cot^2 x+cot^2 x+1−2=0  3cot^2 x−1=0  cotx=±((√3)/3) ⇒tanx=±(√3)  x=±(π/3)+πn , n∈Z
$$\mathrm{2cot}^{\mathrm{2}} \mathrm{x}+\mathrm{csc}^{\mathrm{2}} \mathrm{x}−\mathrm{2}=\mathrm{0} \\ $$$$\mathrm{2cot}^{\mathrm{2}} \mathrm{x}+\mathrm{cot}^{\mathrm{2}} \mathrm{x}+\mathrm{1}−\mathrm{2}=\mathrm{0} \\ $$$$\mathrm{3cot}^{\mathrm{2}} \mathrm{x}−\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{cotx}=\pm\frac{\sqrt{\mathrm{3}}}{\mathrm{3}}\:\Rightarrow\mathrm{tanx}=\pm\sqrt{\mathrm{3}} \\ $$$$\mathrm{x}=\pm\frac{\pi}{\mathrm{3}}+\pi\mathrm{n}\:,\:\mathrm{n}\in\mathbb{Z} \\ $$

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