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  • Find the value of <img alt="\cos^{-1}(\cos\frac{4\pi}{3})+\sin^{-1}(\sin\frac{4\pi}{3})" src="http://entrancecorner.oncodecogs.com/gif.latex?%5Ccos%5E%7B-1%7D%28%5Ccos%5Cfrac%7B4%5Cpi%7D%7B3%7

Find the value of \cos^{-1}(\cos\frac{4\pi}{3})+\sin^{-1}(\sin\frac{4\pi}{3})

Option: 1

\frac{4\pi}{3}


Option: 2

-\frac{4\pi}{3}


Option: 3

-\frac{\pi}{2}


Option: 4

\frac{\pi}{3}


Answers (1)

best_answer

\\\cos^{-1}(\cos\frac{4\pi}{3})+\sin^{-1}(\sin\frac{4\pi}{3})\\ =\cos^{-1}(\cos(2\pi-\frac{2\pi}{3}))+\sin^{-1}(\sin(\pi+\frac{\pi}{3}))\\ =\cos^{-1}(\cos(\frac{2\pi}{3}))+\sin^{-1}(-\sin(\frac{\pi}{3}))\\ =\cos^{-1}(\cos(\frac{2\pi}{3}))+\sin^{-1}(\sin(-\frac{\pi}{3}))\\ =\frac{2\pi}{3}-\frac{\pi}{3}\\ =\frac{\pi}{3}

Posted by

avinash.dongre

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