The value of $ \sin ^{-1} \sin 17+\cos ^{-1} \cos 10 $ is equal to

Question

The value of $ \sin ^{-1} \sin 17+\cos ^{-1} \cos 10 $ is equal to, $ 27 $, $ -27 $, $ 17-5 \pi $, $ 9 \pi-27 $

MARKS App · Accepted Answer

sin - 1 ⁡ sin ⁡ 17 = sin - 1 ⁡ sin ⁡ 17 - 5 π + 5 π = 5 π - 17 cos - 1 ⁡ cos ⁡ 10 = cos - 1 ⁡ cos ⁡ 10 - 3 π + 3 π = cos - 1 ⁡ cos ⁡ 3 π + 10 - 3 π = cos - 1 ⁡ - cos ⁡ 10 - 3 π = π - cos - 1 ⁡ cos ⁡ 10 - 3 π = π - 10 - 3 π = 4 π - 10 Hence, sin - 1 ⁡ sin ⁡ 17 + cos - 1 ⁡ cos ⁡ 10 = 9 π - 27

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