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प्रश्न
Find the principal value of the following:
`cos^(-1) (-1/sqrt2)`
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उत्तर
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].
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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