Listen NCERT Audio Books to boost your productivity and retention power by 2X.
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 350°) – sin–1(sin 350°).
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°