The value of \( \sec \left[\sin ^{-1}\left(-\sin \frac{50 \pi}{9}\right)+\cos ^{-1} \cos \left(-...

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The value of \( \sec \left[\sin ^{-1}\left(-\sin \frac{50 \pi}{9}\right)+\cos ^{-1} \cos \left(-\frac{31 \pi}{9}\right)\right] \) is equal to
(A) \( \sec \frac{10 \pi}{9} \)
(B) 1
(C) \( \sec \frac{\pi}{9} \)
(D) \( -1 \)
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