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Question Number 146230 by mathdanisur last updated on 12/Jul/21

(1/(cos^2 (x))) - 1 + (1/(cos(x))) = 1 ⇒ x=?

$$\frac{\mathrm{1}}{{cos}^{\mathrm{2}} \left({x}\right)}\:-\:\mathrm{1}\:+\:\frac{\mathrm{1}}{{cos}\left({x}\right)}\:=\:\mathrm{1}\:\Rightarrow\:{x}=? \\ $$

Answered by qaz last updated on 12/Jul/21

sec^2 x−1+sec x=1  ⇒sec^2 x+sec x−2=0  ⇒sec x=−2 or 1  ⇒cos x=−(1/2)  or 1  ⇒x=kπ±(π/3) or 2kπ.....(k∈Z)

$$\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}−\mathrm{1}+\mathrm{sec}\:\mathrm{x}=\mathrm{1} \\ $$$$\Rightarrow\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}+\mathrm{sec}\:\mathrm{x}−\mathrm{2}=\mathrm{0} \\ $$$$\Rightarrow\mathrm{sec}\:\mathrm{x}=−\mathrm{2}\:\mathrm{or}\:\mathrm{1} \\ $$$$\Rightarrow\mathrm{cos}\:\mathrm{x}=−\frac{\mathrm{1}}{\mathrm{2}}\:\:\mathrm{or}\:\mathrm{1} \\ $$$$\Rightarrow\mathrm{x}=\mathrm{k}\pi\pm\frac{\pi}{\mathrm{3}}\:\mathrm{or}\:\mathrm{2k}\pi.....\left(\mathrm{k}\in\mathbb{Z}\right) \\ $$

Commented by mathdanisur last updated on 12/Jul/21

cool Ser thanks

$${cool}\:{Ser}\:{thanks} \\ $$

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