Q. 215.0( 1 Vote )

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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