Evaluate the following.

​$$\cos^{-1}\left(\frac{1}{\sqrt{2}}\right) + \sec^{-1}\left(-\sqrt{2}\right)$$

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Correct option is A

Given:

$$\cos^{-1}\left(\frac{1}{\sqrt{2}}\right) + \sec^{-1}\left(-\sqrt{2}\right)$$

Solution:

Evaluate the inverse cosine function:

​$$\cos^{-1}\left(\frac{1}{\sqrt{2}}\right)$$ = $$\frac {\pi}{4}$$

Evaluate the inverse secant function:

​$$\sec^{-1}\left(-\sqrt{2}\right)$$ = $$\frac{ 3\pi}{4}$$

So, 

​$$\cos^{-1}\left(\frac{1}{\sqrt{2}}\right) + \sec^{-1}\left(-\sqrt{2}\right)$$ = $$\frac {\pi}{4}$$ + $$\frac{ 3\pi}{4}$$ =$$\pi$$

Option (a) is right.

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