# TrigInt - Math 218 Kouba Trig Identities and...

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Unformatted text preview: Math 218 Kouba Trig Identities and Antiderivatives You need NOT memorize identities number 1.) through 4.). 1.) sin(A + B) = sinA cosB + cosA sinB sin(A -— B) = sinA cosB — cosA sinB 2.) 3.) cos(A + B) = cosA cosB — sinA sinB 4.) cos(A — B) = cosA cosB + sinA sinB You MUST memorize the following identities and antiderivatives. 5.) cos2 a: + sin2 :1: = 1 6.) sin 2x = 2sinxcosw 1 2 7.) cos 2:1: = 20052 x — 1 so that cos2 a: = W . . 1 —— cos 2x = 1 — 2 sm2 as so that sm2 :3 = ——-—- 2 = cosza: — sin2 x 8.) 1 + tan2 a: = sec2 9: so that tan2 :1: = sec2 :1: — 1 9.) 1 + cot2 m = csc2 a: so that cot2 a: = csc2 a: — 1 . 1 10.) /cosx d3: = s1nx+C 20.) /1+\$2 dcc = arctanx+C 1 1 11.) /sin:c dm = —cosm+C and /a2+a:2 dz = Earctan§+0 1 12.) /sec2m d1: = tanx+C 21.) /— da: 2 arcsinm+C \/1 — m2 1 , a: 13.) /csczm dx = —cotx+C and /W dac = arcs1nE+C 1 14.) /secx tanm dx = secar+C 22.) ||\/——2—1- d2: = arcseC\$+C x as — 1 1 as 15.) foscm cotm d3: = —cscac+C and /m dz: = garcsecfc 16.) /tanx d2: = 1n|secxi+C 17.) /cotx due 2 1n|sinx|+C 18.) /secx dx :2 ln|secx+tanxl+0 19.) /csca: dac = 1n|csczv—cotzv|+C ...
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