If \( \cot \left(\cos ^{-1} x\right)=\sec \left\{\tan ^{-1}\left(\f...

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If \( \cot \left(\cos ^{-1} x\right)=\sec \left\{\tan ^{-1}\left(\frac{a}{\sqrt{b^{2}-a^{2}}}\right)\right\} \),
\( \mathrm{P} \)
W
then the value of \( x \) is equal to
(A) \( \frac{b}{\sqrt{2 b^{2}-a^{2}}} \)
(B) \( \frac{a}{\sqrt{2 b^{2}-a^{2}}} \)
(C) \( \frac{\sqrt{b^{2}-a^{2}}}{a} \)
(D) \( \frac{\sqrt{b^{2}-a^{2}}}{b} \)
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