Question

\( -\frac{2\pi}{5} \) is the principal value of

• A. \( \sin^{-1}\left[\sin\left(\frac{7\pi}{5}\right)\right] \)
• B. \( \tan^{-1}\left[\tan\left(\frac{7\pi}{5}\right)\right] \)
• C. \( \cos^{-1}\left[\cos\left(\frac{7\pi}{5}\right)\right] \)
• D. \( \sec^{-1}\left[\sec\left(\frac{7\pi}{5}\right)\right] \)

Hint:

For inverse trigonometric functions, always check the principal value range first. The value of \( \sin^{-1}x \) always lies in \( \left[-\frac{\pi}{2},\frac{\pi}{2}\right] \).

Answer 1

The Correct Option is A