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Question
Find the principal value of the following: cos- 1`(-1/2)`
Solution
The principal value branch of cos- 1x [0, π].
Let cos- 1`(-1/2)`= α, where 0 ≤ α ≤ π
∴ cos α = `-1/2 = -cos pi/(3)`
∴ cos α = `cos(pi - pi/3)` ...[∵ cos(π – θ) = – cosθ]
∴ cos α = cos `(2pi)/(3)`
∴ α = `(2pi)/(3) ...[∵ 0 ≤ (2pi)/(3) ≤ pi]`
∴ the principal value of cos- 1`(-1/2) "is" (2pi)/(3)`.
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