Arrange the principal values of the following functions in ascending order

(A) $cosec^{-1}(2)$
(B) $\tan^{-1}(-\sqrt{3})$
(C) $\tan^{-1}(1)$
(D) $\tan^{-1}(\cos\frac{3\pi}{7})$

Choose the correct answer from the options given below:

(B), (D), (A), (C)

The correct answer is Option (3) → (B), (D), (A), (C)

Compute principal values:

(A) $\csc^{-1}(2) = \sin^{-1}(\frac{1}{2}) = \frac{\pi}{6} \approx 0.5236$

(B) $\tan^{-1}(-\sqrt{3}) = -\frac{\pi}{3} \approx -1.0472$

(C) $\tan^{-1}(1) = \frac{\pi}{4} \approx 0.7854$

(D) $\cos\frac{3\pi}{7} \approx 0.2225 \Rightarrow \tan^{-1}(0.2225) \approx 0.219$

Arrange in ascending order:

(B) $< (D) < (A) < (C)$