anonymous
  • anonymous
tan(45+a)-tan(45-a)
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[={(1+tana)/1-tana}-{(1-tana)/1+tana}\]\[{(1+tana)^2-(1-tana)^2}/1-\tan^2a\]\[=4tana/1-\tan^2a\]
anonymous
  • anonymous
Scroll down to "The Other Identities" section at the following web site: http://library.thinkquest.org/20991/alg2/trigi.html There you will find these identities for Tan(A+B) and Tan(A-B): tan (A + B) = (tan A + tan B)/(1 - (tan A)(tan B)) tan (A - B) = (tan A - tan B)/(1 + (tan A)(tan B)) From the problem it is assumed that tan(45) is the tangent of 45 degrees, which is 1. Thus tan(45+a)-tan(45-a) -> \[(1+\tan a)/(1-\tan a)-(1-\tan a/(1+\tan a)\] When he above expression is combined and simplified, the result is: \[2 \tan 2a\] Note: If any one can show that final result is invalid, I'm certain that Wolfram Research would be glad to hear from you.

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