Book: RD Sharma - Mathematics (Volume 1)
Chapter: 4. Inverse Trigonometric Functions
Subject: Maths - Class 12th
Q. No. 21 of Very short answer
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21
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°
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