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Evaluate the following: (i) cos⁻¹(cos(7*pi/6)) (ii) tan⁻¹(tan(3*pi/4))

1. (i) 5*pi/6; (ii) -pi/4
2. (i) 7*pi/6; (ii) 3*pi/4
3. (i) pi/6; (ii) pi/4
4. (i) 5*pi/6; (ii) 3*pi/4

Correct answer: (i) 5*pi/6; (ii) -pi/4

Solution

Apply the principal-value ranges: cos⁻¹(cos x) returns the angle in [0, pi] with the same cosine; tan⁻¹(tan x) returns the angle in (-pi/2, pi/2) with the same tangent.

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