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Question-118506




Question Number 118506 by meireza last updated on 18/Oct/20
Answered by Lordose last updated on 18/Oct/20
(√2)sin(x°+15°)=1  Divide by (√2)  sin(x°+15°)=(1/( (√2)))  take sin^(−1)  of both sides  sin^(−1) (sin(x+15°))=sin^(−1) ((1/( (√2))))  x+15°=45°+360n {n∈N}  x=30°+360n  x=(π/6)+2πn {n∈N}
$$\sqrt{\mathrm{2}}\mathrm{sin}\left(\mathrm{x}°+\mathrm{15}°\right)=\mathrm{1} \\ $$$$\mathrm{Divide}\:\mathrm{by}\:\sqrt{\mathrm{2}} \\ $$$$\mathrm{sin}\left(\mathrm{x}°+\mathrm{15}°\right)=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}} \\ $$$$\mathrm{take}\:\mathrm{sin}^{−\mathrm{1}} \:\mathrm{of}\:\mathrm{both}\:\mathrm{sides} \\ $$$$\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{sin}\left(\mathrm{x}+\mathrm{15}°\right)\right)=\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\right) \\ $$$$\mathrm{x}+\mathrm{15}°=\mathrm{45}°+\mathrm{360n}\:\left\{\mathrm{n}\in\mathbb{N}\right\} \\ $$$$\mathrm{x}=\mathrm{30}°+\mathrm{360n} \\ $$$$\mathrm{x}=\frac{\pi}{\mathrm{6}}+\mathrm{2}\pi\mathrm{n}\:\left\{\mathrm{n}\in\mathbb{N}\right\} \\ $$
Answered by ebi last updated on 18/Oct/20
    (√2)sin (x+15)°=1  sin (x+15)°=(1/( (√2)))  let θ=x+15,  sin θ°=(1/( (√2)))  since the value is positive, the values of θ are situated at quadrant I and II.  therefore,   θ°=45°, 180°−45°,  θ°=45°, 135°    thus,  x+15°=45°, 135°  x=30°, 120° (0°≤x≤360°)
$$ \\ $$$$ \\ $$$$\sqrt{\mathrm{2}}\mathrm{sin}\:\left({x}+\mathrm{15}\right)°=\mathrm{1} \\ $$$$\mathrm{sin}\:\left({x}+\mathrm{15}\right)°=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}} \\ $$$${let}\:\theta={x}+\mathrm{15}, \\ $$$$\mathrm{sin}\:\theta°=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}} \\ $$$${since}\:{the}\:{value}\:{is}\:{positive},\:{the}\:{values}\:{of}\:\theta\:{are}\:{situated}\:{at}\:{quadrant}\:{I}\:{and}\:{II}. \\ $$$${therefore},\: \\ $$$$\theta°=\mathrm{45}°,\:\mathrm{180}°−\mathrm{45}°, \\ $$$$\theta°=\mathrm{45}°,\:\mathrm{135}° \\ $$$$ \\ $$$${thus}, \\ $$$${x}+\mathrm{15}°=\mathrm{45}°,\:\mathrm{135}° \\ $$$${x}=\mathrm{30}°,\:\mathrm{120}°\:\left(\mathrm{0}°\leqslant{x}\leqslant\mathrm{360}°\right) \\ $$

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