\(tan^{-1}(-1)+cos^{-1}(\frac{-1}{\sqrt{2}})\)=?A. \(\frac{\pi}{2}\)B

1.	\(tan^{-1}(-1)+cos^{-1}(\frac{-1}{\sqrt{2}})\)=?A. \(\frac{\pi}{2}\)B. \(\pi\)C. \(\frac{3\pi}{2}\)D. \(\frac{2\pi}{3}\)
Answer» Correct Answer is (A) \(\frac{\pi}{2}\) Let , x = \(tan^{-1}(-1)+cos^{-1}(\frac{-1}{\sqrt{2}})\) ⇒ x= \(tan^{-1}(-1)+(\pi-cos^{-1}(\frac{-1}{\sqrt{2}}))\) \(\because tan^{-1}(-\theta)=-tan^{-1}(\theta)\) and \(cos^{-1}(-\theta)=\pi-cos^{-1}(\theta))\) ⇒ x= \(-\frac{\pi}{4}\)\(+(\pi-\frac{\pi}{4})\) ⇒ x= \(-\frac{\pi}{4}\)+\(\frac{3\pi}{4}\) ⇒ x= \(\frac{\pi}{2}\)

\(tan^{-1}(-1)+cos^{-1}(\frac{-1}{\sqrt{2}})\)=?A. \(\frac{\pi}{2}\)B. \(\pi\)C. \(\frac{3\pi}{2}\)D. \(\frac{2\pi}{3}\)

Answer»

Correct Answer is (A) \(\frac{\pi}{2}\)

Let , x = \(tan^{-1}(-1)+cos^{-1}(\frac{-1}{\sqrt{2}})\)

⇒ x= \(tan^{-1}(-1)+(\pi-cos^{-1}(\frac{-1}{\sqrt{2}}))\)

\(\because tan^{-1}(-\theta)=-tan^{-1}(\theta)\) and \(cos^{-1}(-\theta)=\pi-cos^{-1}(\theta))\)

⇒ x= \(-\frac{\pi}{4}\)\(+(\pi-\frac{\pi}{4})\)

⇒ x= \(-\frac{\pi}{4}\)+\(\frac{3\pi}{4}\)

⇒ x= \(\frac{\pi}{2}\)