Find the principal values ofCOSI (- )cosTV2

1.	Find the principal values ofCOSI (- )cosTV2
Answer» 3pi/4 since cosinv(-x) = pi - cosinv(x) If the principal value of cos−1 x is θ then we know, 0 ≤ θ ≤ π. Therefore, If the principal value of cos−1 (-1/√2) be θ then cos−1 (-1/√2) = θ ⇒ cos θ = (-1/√2) = cos π/4 = cos (π - π/4) [Since, 0 ≤ θ ≤ π] Therefore, the principal value of cos−1 (-1/√2) is π - π/4 = 3π/4

Answer»

3pi/4 since cosinv(-x) = pi - cosinv(x)

If the principal value of cos−1 x is θ then we know, 0 ≤ θ ≤ π.

Therefore, If the principal value of cos−1 (-1/√2) be θ then cos−1 (-1/√2) = θ

⇒ cos θ = (-1/√2) = cos π/4 = cos (π - π/4) [Since, 0 ≤ θ ≤ π]

Therefore, the principal value of cos−1 (-1/√2) is π - π/4 = 3π/4

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