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sir, ln(tan(90-x)) is writtn as -ln(tanx) and - is removed out of integration and then both the integration are added which makes 2i=0, so i=0

sir, instead of this if we write ln(tan(90-x)) as ln(cot(x)) and then add both the integration an writing ln(tan(x))+ln(cot(x)) as ln(tan(x)*cot(x)) as ln1, so following these steps we get 2i=integration 0, so i=1

is coming from this procedure,

so why both the answers are coming different please explain me or if i am doing something wrong please correct me

qsnImg
Asked by jaychandran1967 19th October 2018, 4:31 PM
Answered by Expert
Answer:
begin mathsize 18px style straight I equals integral sin 2 straight x space ln space open parentheses tan open parentheses straight x close parentheses close parentheses dx
straight I equals integral sin 2 straight x space ln open parentheses space tan open parentheses 90 minus straight x close parentheses close parentheses dx equals integral sin 2 straight x space ln space open parentheses cotx space close parentheses dx
2 straight I space equals space integral sin 2 straight x space ln space open parentheses cotx cross times tanx close parentheses space dx
2 straight I equals integral sin 2 straight x space ln space open parentheses 1 close parentheses space dx
2 straight I space equals space 0............. ln space open parentheses 1 close parentheses equals 0
straight I space equals space 0 end style
Answered by Expert 22nd October 2018, 5:05 PM
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