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Question Number 10155 by Tawakalitu ayo mi last updated on 27/Jan/17

solve for x  sin(x) − (√(3cos(x))) = 1

$$\mathrm{solve}\:\mathrm{for}\:\mathrm{x} \\ $$$$\mathrm{sin}\left(\mathrm{x}\right)\:−\:\sqrt{\mathrm{3cos}\left(\mathrm{x}\right)}\:=\:\mathrm{1} \\ $$

Answered by mrW1 last updated on 28/Jan/17

sin (x)=1+(√(3cos (x)))≥1  ⇒sin (x)=1 and cos (x)=0  ⇒x=(π/2)+2nπ, n∈Z

$$\mathrm{sin}\:\left({x}\right)=\mathrm{1}+\sqrt{\mathrm{3cos}\:\left({x}\right)}\geqslant\mathrm{1} \\ $$$$\Rightarrow\mathrm{sin}\:\left({x}\right)=\mathrm{1}\:{and}\:\mathrm{cos}\:\left({x}\right)=\mathrm{0} \\ $$$$\Rightarrow{x}=\frac{\pi}{\mathrm{2}}+\mathrm{2}{n}\pi,\:{n}\in\mathbb{Z} \\ $$

Commented by Tawakalitu ayo mi last updated on 28/Jan/17

God bless you sir.

$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$

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