Find the value of tan-11-cos-1-12-sin-112

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Standard XII

Mathematics

Domain and Range of Basic Inverse Trigonometric Functions

Find the valu...

Question

Find the value of ${tan}^{- 1} 1 + {cos}^{- 1} - \frac{1}{2} + {sin}^{- 1} \frac{1}{2}$

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Solution

@page { margin: 2cm } p { margin-bottom: 0.25cm; line-height: 120% }
${tan}^{- 1} (1) + {cos}^{- 1} (\frac{- 1}{2}) + {sin}^{- 1} (\frac{1}{2})$

$= \frac{π}{4} + π - {cos}^{- 1} (\frac{1}{2}) + \frac{π}{6}$

$= \frac{π}{4} + π - \frac{π}{3} + \frac{π}{6}$

$= \frac{5 π}{4} - \frac{π}{3} + \frac{π}{6}$

$\frac{5 π}{4} - \frac{π}{6}$

$= \frac{15 π - 2 π}{12}$

$= \frac{13 π}{12}$

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Find the value of tan−11+cos−1−12+sin−112

@page { margin: 2cm } p { margin-bottom: 0.25cm; line-height: 120% } tan−1(1)+cos−1(−12)+sin−1(12) =π4+π−cos−1(12)+π6 =π4+π−π3+π6 =5π4−π3+π6 5π4−π6 =15π−2π12 =13π12

Find the value of ${tan}^{- 1} 1 + {cos}^{- 1} - \frac{1}{2} + {sin}^{- 1} \frac{1}{2}$