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STD 12 - 7.1 inderfinite integral — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {{{(\tan x - \cot x)}^2}\;dx = } $
  • A
    $\tan x + \cot x + c$
  • B
    $\sec x\tan x + c$
  • C
    $\cos {\rm{ec}}x\cot x + c$
  • ✓
    None of these
✓

Answer

Correct option: D.
None of these
d
(d)$\int_{}^{} {{{(\tan x - \cot x)}^2}dx} = \int_{}^{} {({{\tan }^2}x + {{\cot }^2}x - 2)\,dx} $
$ = \int_{}^{} {{{\sec }^2}x\,dx} + \int_{}^{} {{\rm{cose}}{{\rm{c}}^{\rm{2}}}x\,dx} - \int_{}^{} {4\,dx} $
$ = \tan x - \cot x - 4x + c.$

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