The principal value of \cos ^{-1} (\frac{1}{2}) + \sin ^{-1} (- {1}/{\sqrt{2}}) is

CBSE Class 12 Math 2022 Term I Solved Paper - Question 7

Question : 7 of 50

Marks: +1, -0

The principal value of

\cos ^{-1} (\;{1}/{2}) + sin \;^{-1} (-\;{1}/{{√{2}}})

Solution:

Explanation:

\cos ^{-1} (\;{1}/{2}) \;+ sin \;^{-1} (\;{-1}/{{√{2}}})

\;=\cos ^{-1} (\cos \;{π}/{3}) - sin \;^{-1} (\;{1}/{{√{2}}})

\;=\;{π}/{3}- sin \;^{-1} ( sin \;\;{π}/{4})

\;=\;{π}/{3}-\;{π}/{4}=\;{π}/{12}

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