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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