Pythagorean Identities? - Printable Version +- School Survival Forums (http://forums.school-survival.net) +-- Forum: Learning, Youth Rights and School Survival (/forumdisplay.php?fid=3) +--- Forum: Homework Help & Answers (/forumdisplay.php?fid=30) +--- Thread: Pythagorean Identities? (/showthread.php?tid=5096) Pythagorean Identities? - Dreamer567 - 03-25-2010 12:27 PM Can someone please verify these problems for me? I will be eternally grateful! (The little 2 after the "tan + 1" means squared) 1) tan + cot= sec(csc) 2) (tan + 1)2 - sec= 2tan Re: Pythagorean Identities? - genuine anarchist - 03-27-2010 03:19 PM Sorry if this is overdue; I learned this last year in precalculus: 1) tan + cot = sec (csc) tan=sin/cos, cot=cos/sin, sec=1/cos, csc=1/sin (sin/cos) + (cos/sin) = (1/cos)(1/sin) >substitute values from other identities ((sin/cos) + (cos/sin) = (1/cos)(1/sin)) (cos) >multiply whole equation by cos (sin2/sincos) + (cos2/sincos) = (1/cos)(1/sin) [the 2 means "squared] (sincos) ((sin2/sincos) +(cos2/sincos) = (1/sincos)) >multiply whole equation by sincos to cancel out the denominator answer: you are left with sin2 + cos2 = 1, a fundamental pythagorean identity 2) (tan +1)2 - sec = 2tan tan2+1=sec2, tan=sin/cos, sec-1/cos tan2 + 2tan + 1 -sec = 2tan