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4-sin-x-2-cos-x-2-1-x-




Question Number 205217 by hardmath last updated on 13/Mar/24
4 sin (x/2) ∙ cos (x/2) = 1  ⇒ x = ?
$$\mathrm{4}\:\mathrm{sin}\:\frac{\mathrm{x}}{\mathrm{2}}\:\centerdot\:\mathrm{cos}\:\frac{\mathrm{x}}{\mathrm{2}}\:=\:\mathrm{1} \\ $$$$\Rightarrow\:\mathrm{x}\:=\:? \\ $$
Answered by A5T last updated on 13/Mar/24
2sinx=2sin((x/2)+(x/2))=4sin((x/2))cos((x/2))=1  ⇒sinx=(1/2)⇒x=30°+360n;150°+360n
$$\mathrm{2}{sinx}=\mathrm{2}{sin}\left(\frac{{x}}{\mathrm{2}}+\frac{{x}}{\mathrm{2}}\right)=\mathrm{4}{sin}\left(\frac{{x}}{\mathrm{2}}\right){cos}\left(\frac{{x}}{\mathrm{2}}\right)=\mathrm{1} \\ $$$$\Rightarrow{sinx}=\frac{\mathrm{1}}{\mathrm{2}}\Rightarrow{x}=\mathrm{30}°+\mathrm{360}{n};\mathrm{150}°+\mathrm{360}{n} \\ $$

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