#### Confirm Action

Are you sure you wish to do this? Member Login Site Notices [Video] - ARFCOM Does the News?!?!?
11/20/2019 5:07:11 PM [ARCHIVED THREAD] - DELETE PLEASE  Joined Feb 2013 Posts 63 EE Offline OK, USA Posted: 10/20/2013 10:13:14 AM EST [Last Edit: 10/20/2013 4:55:41 PM EST by chenault] DELETE PLEASE  Joined Feb 2013 Posts 64 EE Offline OK, USA  Posted: 10/20/2013 10:43:44 AM EST I think that I have number 1 can someone please check. step 1) cosx/1+sinx (sin x is the same as 1+sin x so I multiply times the recipical 1-sin x) step 2) cosx (1-sinx)/(1+sinx)(1-sinx) which breaks down into cosx(1-sinx)/(1-sinx^2) step 3) because 1-sinx^2 is the same as 1+cos^2 I have 1+cos^2 which foiled out is (1+cos)(1+cos) so now my problem looks like thus cosx(1-sinx)/(1+cosx)(1+cosx) step 4) the cosx on the numerator and denominator cancel out and I am left with (1-sinx)/(1+cosx) which is the same as (1/cosx) - (sinx/cosx) which equals (secx)-(tanx) correct?  Joined Nov 2008 Posts 188 EE Offline FL, USA  Posted: 10/20/2013 11:42:26 AM EST  Quote HistoryOriginally Posted By chenault: I think that I have number 1 can someone please check. step 1) cosx/1+sinx (sin x is the same as 1+sin x so I multiply times the recipical 1-sin x) step 2) cosx (1-sinx)/(1+sinx)(1-sinx) which breaks down into cosx(1-sinx)/(1-sinx^2) step 3) because 1-sinx^2 is the same as 1+cos^2 I have 1+cos^2 which foiled out is (1+cos)(1+cos) so now my problem looks like thus cosx(1-sinx)/(1+cosx)(1+cosx) step 4) the cosx on the numerator and denominator cancel out and I am left with (1-sinx)/(1+cosx) which is the same as (1/cosx) - (sinx/cosx) which equals (secx)-(tanx) correct?View Quote No. Your math has a series of errors. (1 + cos X)^2 does not = 1 + cos^2 x, but rather = 1 + 2 (cos x) + cos^2 x. Also, there is no cos x in the denominator to cancel out. Solution: Starting with the initial equation: cosx/(1+sinx) = secx-tanx rewrite everything in terms of cos and sin: cos x / (1 + sin x) = (1 /cos x) - (sin x / cos x) simplifying the right side becomes (1 - sin x)/ cos x so: cos x / (1 + sin x) = (1 - sin x) / cos x multiply both sides by (cos x) (1 + sin x) to get the same denominators, and simplifying gives us cos x * cos x = (1 + sin x) (1 - sin x) cos^2 x = 1 - sin^2 x and then adding sin^2x to both sides cos^2 x + sin^2 x = 1 since this is true, we prove the original equality.  Joined Feb 2012 Posts 2024 EE Offline TN, USA  Posted: 10/27/2013 4:27:43 AM EST [Last Edit: 10/27/2013 4:29:22 AM EST by switchtanks] wrong thread [ARCHIVED THREAD] - DELETE PLEASE Top Top