Question:
The value of \(\sin^{-1}\left(\cos\left(\dfrac{33\pi}{5}\right)\right)\) is
\(\sin^{-1}\left(\cos\left(\dfrac{33\pi}{5}\right)\right)\) का मान क्या है?
Options:
- \(\dfrac{-7\pi}{5}\)
- \(\dfrac{3\pi}{5}\)
- \(\dfrac{\pi}{10}\)
- \(\dfrac{-\pi}{10}\)
- \(\dfrac{-7\pi}{5}\)
- \(\dfrac{3\pi}{5}\)
- \(\dfrac{\pi}{10}\)
- \(\dfrac{-\pi}{10}\)
Correct Answer: d)
Explanation:
\(\dfrac{33\pi}{5} = 6\pi + \dfrac{3\pi}{5}\).
\(\cos\left(\dfrac{33\pi}{5}\right) = \cos\left(\dfrac{3\pi}{5}\right) = \sin\left(\dfrac{\pi}{2} – \dfrac{3\pi}{5}\right) = \sin\left(-\dfrac{\pi}{10}\right)\).
\(\sin^{-1}\left(\sin\left(-\dfrac{\pi}{10}\right)\right) = -\dfrac{\pi}{10}\).
\(\cos(33\pi/5) = \cos(3\pi/5) = \sin(-\pi/10)\)।
अतः \(\sin^{-1}(\sin(-\pi/10)) = -\dfrac{\pi}{10}\)।