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Question
Find the principal value of `cos^(-1) (-1/sqrt2)`
Solution
Let `cos^(-1)(-1/sqrt2) = y` Then `cos y = - 1/sqrt2 = -cos (pi/4) = cos(pi - pi/4) = cos((3pi)/4)`
We know that the range of the principal value branch of cos−1 is [0,π] and
Where `(3pi)/4 ∈ [0, pi]`
cos `((3pi)/4) = - 1/sqrt2`
Therefore, the principal value of `cos^(-1) (-1/sqrt2)` is `(3pi)/4`
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