Answer each of the following questions in one word or one sentence or as per exact requirement of the question:

Write the value of cos^{–1}(cos 1540°).

Given cos^{-1} (cos 1540°)

= cos^{-1}{cos (1440° + 100°)}

= cos^{-1}{cos (360° × 4 + 100°)}

We know that cos (2π + θ) = cos θ

= cos^{-1}{cos 100°}

We know that cos^{-1} (cos θ) = θ if θ ∈ [0, π]

= 100°

∴ cos^{-1} (cos 1540°) = 100°

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