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CBSE Class 12-science Answered

evaluate Integration sin( x – α)/sin(x + α) dx explain in great detail
Asked by haroonrashidgkp | 22 Sep, 2018, 11:42: PM
answered-by-expert Expert Answer
begin mathsize 18px style integral fraction numerator sin open parentheses straight x minus straight alpha close parentheses over denominator sin open parentheses straight x plus straight alpha close parentheses end fraction dx
equals integral fraction numerator begin display style sin open parentheses straight x plus straight alpha minus 2 straight alpha close parentheses end style over denominator begin display style sin open parentheses straight x plus straight alpha close parentheses end style end fraction dx
equals integral fraction numerator begin display style sin open parentheses straight x plus straight alpha close parentheses cos 2 straight alpha minus cos open parentheses straight x plus straight alpha close parentheses sin 2 straight alpha end style over denominator begin display style sin open parentheses straight x plus straight alpha close parentheses end style end fraction dx
equals integral cos 2 straight alpha space dx space minus space integral fraction numerator begin display style cos open parentheses straight x plus straight alpha close parentheses sin 2 straight alpha end style over denominator begin display style sin open parentheses straight x plus straight alpha close parentheses end style end fraction dx
equals straight x. cos 2 straight alpha space minus space sin 2 straight alpha integral fraction numerator begin display style cos open parentheses straight x plus straight alpha close parentheses end style over denominator begin display style sin open parentheses straight x plus straight alpha close parentheses end style end fraction dx
put space sin open parentheses straight x plus straight alpha close parentheses equals straight t
straight I space equals space straight x. cos 2 straight alpha space minus space sin 2 straight alpha space ln open parentheses sin open parentheses straight x plus straight alpha close parentheses close parentheses plus straight c end style
Answered by Arun | 24 Sep, 2018, 11:35: AM
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