find the value of sin[ π\pi /6-1/sin(- −3\sqrt{-3}/2)]

asked by guest
on Dec 04, 2024 at 12:56 am



You asked:

Evaluate the expression: sin⁡(π6−1sin⁡(−−32))\sin\left( \frac{\pi}{6} - \frac{1}{\sin\left( \frac{-\sqrt{-3}}{2} \right)} \right)

MathBot Answer:

sin⁡(π6−1sin⁡(−−32))=sin⁡(π6−isinh⁡(32))\sin\left( \frac{\pi}{6} - \frac{1}{\sin\left( \frac{-\sqrt{-3}}{2} \right)} \right) = \sin{\left(\frac{\pi}{6} - \frac{i}{\sinh{\left(\frac{\sqrt{3}}{2} \right)}} \right)}

sin⁡(π6−1sin⁡(−−32))=sin⁡(π6−1sin⁡(−⋅−3⋅12))=sin⁡(π6−1sin⁡(−⋅i⋅3⋅12))=sin⁡(π6−1sin⁡(−12⋅i⋅3))=sin⁡(π6−1−⋅i⋅sinh⁡(12⋅3))=sin⁡(π6−i⋅1sinh⁡(12⋅3))\begin{aligned}\sin\left( \frac{\pi}{6} - \frac{1}{\sin\left( \frac{-\sqrt{-3}}{2} \right)} \right)&=\sin{\left(\frac{\pi}{6} - \frac{1}{\sin{\left(- \cdot \sqrt{-3} \cdot \frac{1}{2} \right)}} \right)}\\&=\sin{\left(\frac{\pi}{6} - \frac{1}{\sin{\left(- \cdot i \cdot \sqrt{3} \cdot \frac{1}{2} \right)}} \right)}\\&=\sin{\left(\frac{\pi}{6} - \frac{1}{\sin{\left(- \frac{1}{2} \cdot i \cdot \sqrt{3} \right)}} \right)}\\&=\sin{\left(\frac{\pi}{6} - \frac{1}{- \cdot i \cdot \sinh{\left(\frac{1}{2} \cdot \sqrt{3} \right)}} \right)}\\&=\sin{\left(\frac{\pi}{6} - i \cdot \frac{1}{\sinh{\left(\frac{1}{2} \cdot \sqrt{3} \right)}} \right)}\end{aligned}

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