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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