Question:
The value of \(\cot\left[\dfrac{1}{2}\sin^{-1}\dfrac{\sqrt{3}}{2}\right]\) is
\(\cot\left[\dfrac{1}{2}\sin^{-1}\dfrac{\sqrt{3}}{2}\right]\) का मान क्या है?
Options:
- \(\dfrac{1}{\sqrt{3}}\)
- 0
- 1
- \(\sqrt{3}\)
- \(\dfrac{1}{\sqrt{3}}\)
- 0
- 1
- \(\sqrt{3}\)
Correct Answer: d)
Explanation:
\(\sin^{-1}\left(\dfrac{\sqrt{3}}{2}\right) = \dfrac{\pi}{3}\).
\(\cot\left[\dfrac{1}{2} \cdot \dfrac{\pi}{3}\right] = \cot\left(\dfrac{\pi}{6}\right) = \sqrt{3}\).
\(\sin^{-1}\left(\dfrac{\sqrt{3}}{2}\right) = \dfrac{\pi}{3}\)।
\(\cot\left(\dfrac{\pi}{6}\right) = \sqrt{3}\)।