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Write the value of cos–1(cos 350°) – sin–1(sin 350°). |
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Answer» Given cos-1 (cos 350°) – sin-1 (sin 350°) = cos -1 [cos (360° - 10°)] – sin-1 (sin (360° - 10°)] We know that cos (2π – θ) = cos θ and sin (2π – θ) = -sin θ = cos-1 (cos 10°) – sin-1 (-sin 10°) We know that cos-1 (cos θ), if θ ∈ [0, π] and sin (-θ) = -sin θ = 10° - sin-1 (sin (-10°)) We know that sin-1 (sin θ) = θ, if θ ∈ [-π/2, π/2] = 10° - (-10°) = 10° + 10° = 20° ∴ cos-1 (cos 350°) – sin -1 (sin 350°) = 20° |
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