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Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
MCQ
Find the value of $:\ \sec^2 (\tan^{-1} 2) +\csc^2 (\cot^{-1} 3)$
  • A
    $11$
  • ✓
    $15$
  • C
    $17$
  • D
    $21$
✓

Answer

Correct option: B.
$15$
$ \sec^2 (\tan^{-1} 2) +\csc^2 (\cot^{-1} 3)$
$ =1+\tan^2 (\tan^{-1} 2) +1+\cot^2 (\cot^{-1} 3)$
$ =1+[\tan (\tan^{-1} 2)]^2 +1+[\cot (\cot^{-1} 3)]^2$
$ =1+2^2+1+3^2=15$

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