Evaluate:
 
 
integral subscript 0 superscript pi divided by 2 end superscript space cos 2 x space d x divided by cos x

Asked by ahuja8087 | 11th Nov, 2016, 06:14: PM

Expert Answer:

begin mathsize 16px style integral subscript 0 superscript straight pi divided by 2 end superscript fraction numerator cos 2 straight x space over denominator cosx end fraction dx space
equals space integral subscript 0 superscript straight pi divided by 2 end superscript fraction numerator left parenthesis 2 cos squared straight x space plus 1 right parenthesis space over denominator cosx end fraction dx space
equals space integral subscript 0 superscript straight pi divided by 2 end superscript open parentheses 2 cosx plus 1 over cosx close parentheses dx space
space equals space integral subscript 0 superscript straight pi divided by 2 end superscript open parentheses 2 cosx plus secx close parentheses dx space
space equals 2 space integral subscript 0 superscript straight pi divided by 2 end superscript cosx space dx space plus space space integral subscript 0 superscript straight pi divided by 2 end superscript space secx space dx space
space equals space 2 left square bracket sinx right square bracket subscript 0 to the power of straight pi divided by 2 end exponent plus open square brackets ln open vertical bar secx plus tanx close vertical bar close square brackets subscript 0 to the power of straight pi divided by 2 end exponent
space equals space 2 open parentheses sin straight pi over 2 minus sin space 0 close parentheses plus open parentheses ln open vertical bar sec straight pi over 2 plus tan straight pi over 2 close vertical bar space minus ln open vertical bar sec 0 plus tan 0 close vertical bar space close parentheses
equals 2 left parenthesis 1 space minus space 0 right parenthesis plus open parentheses ln open vertical bar bold sec bold pi over bold 2 plus bold tan bold pi over bold 2 close vertical bar space minus ln open vertical bar sec 0 plus tan 0 close vertical bar space close parentheses
Observe space that space sec straight pi over 2 space and space tan straight pi over 2 space are space not space defined.
So comma space this space question space seems space to space be space incorrect. end style

Answered by Rebecca Fernandes | 12th Nov, 2016, 09:41: AM