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Question:

Write the principal value of cos(1/2) - 2sin(π/4)

Solution:

The principal value of cos⁻¹x lies in [0, π] and that of sin⁻¹x lies in [-π/2, π/2]
→cos⁻¹(1/2) = π/3 and sin⁻¹(π/4) = -π/6
Substituting these values in the final equation, we get π/3 + π/3 = 2π/3