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Find the principal value of the following (i) `cos^(-1) (cos 3)` (ii) `cos^(-1) (cos 4)` (iii) `cos^(-1) (cos 15)` (iv) `cos^(-1) (cos 30)` (v) `cos^(-1) (cos 50)` (vi) `cos^(-1) (cos.(48pi)/(7))` |
Answer» (i) Since `3 in [0, pi], cos^(-1) (cos 3) = 3` (ii) Since `4 !in [0, pi], cos^(-1) (cos 4) != 4` `:. Cos^(-1) (cos 4) = 2pi - 4` (iii) `cos^(-1) (cos 15) = 15 - 4 pi` (iv) `cos^(-1) (cos 30) = 10 pi - 30` (v) `cos^(-1) (cos 50) = 16 pi - 50` (vi) `cos^(-1) (cos.(48pi)/(7)) = cos^(-1) (cos(6pi + (6pi)/(7)))` `= cos^(-1) (cos.(6pi)/(7)) = (6pi)/(7)` |
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