tag:blogger.com,1999:blog-8522480567895316400.post657815226746991317..comments2023-10-21T01:24:15.766+11:00Comments on 2007 Exams Preperation: A 'Not so simple' Trig ProblemUnknownnoreply@blogger.comBlogger3125tag:blogger.com,1999:blog-8522480567895316400.post-16209144806242031512007-10-28T21:59:00.000+11:002007-10-28T21:59:00.000+11:00IB believe in using the most explicit and fastest ...IB believe in using the most explicit and fastest ways of obtaining answers. Hence no splitting of Tan was used in this problem (Biggest hint ever)David Jinhttps://www.blogger.com/profile/02620475596363156624noreply@blogger.comtag:blogger.com,1999:blog-8522480567895316400.post-9789882660839694992007-10-28T16:57:00.000+11:002007-10-28T16:57:00.000+11:00Lol... Ok firstly, sort of scared to try your ques...Lol... Ok firstly, sort of scared to try your questions now, not sure if what I know on my syllabus even covers everything I should know to solve this. <BR/><BR/>Anyway, this is how far I got... Please assume all intergrals from 0 to Pi/4, I won't sub the values to the end (which I haven't come to yet)<BR/><BR/>From int(tan(x) - (tan(x)-1)/(tan(x)+1))<BR/><BR/>= -ln(cos(x)) - int((tan(x)-1)/(tan(x)+1))<BR/><BR/>(Split the tan(x)'s into sin(x)/cos(x)) <BR/><BR/>= -ln(cos(x)) - int((sin(x)-cos(x))/(sin(x)+cos(x))<BR/><BR/>(Used a shitload of identities here, including multiplying by conjugate, sin^2(x)+cos^2(x)=1, 2sin(x)cos(x) = sin(2x), sin^2(x)-cos^2(x)=-cos(2x))<BR/><BR/>= -ln(cos(x)) + int((1-sin(2x))/(cos2x))<BR/><BR/>Which then left me with a problem... I have no idea how to integrate sec(2x). At this point I gave up, perhaps you could help by telling me how I do that, or (more likely) where I went wrong? <BR/><BR/>P.S I think this is wrong, checking with online integrators gave me answers so horrific that I got scared out of studying and into playing games. <BR/><BR/>Don't bother with mathtype imo, I can understand calculator format ^^Glenhttps://www.blogger.com/profile/17637046924470445525noreply@blogger.comtag:blogger.com,1999:blog-8522480567895316400.post-5403312958228804622007-10-28T00:08:00.000+10:002007-10-28T00:08:00.000+10:00Btw the answer is ......Ln(2)Yep. How gay is that....Btw the answer is ...<BR/><BR/>...<BR/><BR/>Ln(2)<BR/><BR/>Yep. How gay is that.David Jinhttps://www.blogger.com/profile/02620475596363156624noreply@blogger.com