Doing 100 trig identity problems in one take (finally!!!)
Get the problem & answer files: https://www.patreon.com/blackpenredpen/posts/100-trig-167729637In this 5-hour math marathon, we solve 100 essential trig identity problems you need to know master. Whether you are reviewing for Pre-Calculus or preparing for Calculus (especially integration techniques in Calculus 2), mastering these algebraic manipulations and identities will give you the ultimate foundation.
I decided to stop after 1 hour and do it better the next day... https://www.patreon.com/blackpenredpen/posts/after-1-hour-i-168921042 (this post also includes the first 28 questions worksheet)
0:00 Finally, 100 trig identities in one take!
Q1, 01:18, sin(x)sec(x)
Q100, 02:03, Integral Ready Form: csc^4(x)
Q2, 07:06, sin^2(x)/(1-cos(x))
Q3, 09:23, sin(x)/cos^2(x)
Q4, 10:48, cos(x)-sin^2(x)cos(x)
Q5, 12:15, sec(x)-tan(x)sin(x)
Q6, 13:23, (tan(x)+cot(x))/sec(x)
Q7, 15:20, cos(pi-x)
Q8, 20:48, tan(x)+cot(x)
Q9, 22:16, (1-sin^2(x))/cot^2(x)
Q10, 23:16, 1/tan(pi/2-x)
Q11, 26:00, sin(-x)csc(x)
Q12, 28:35, sin^2(x)+cos^2(x)+tan^2(x)
Q13, 30:51, sec(-x)
Q14, 31:20, sin^2(-x)
Q15, 32:16, arccos(x)+arccos(-x)
Q16, 38:47, arcsec(x)
Q17, 43:38, (sin(x)+sin(2x))/(1+cos(x)+cos(2x))
Q18, 48:50, cos(2x)/(cos(x)+sin(x))
Q19, 50:45, (1-tan^2(x))/(1+tan^2(x))
Q20, 52:48, (1-sin(x))/cos(x)
Q21, 55:12, 1/(1-sin(x))+1/(1+sin(x))
Q22, 56:51, (sin(x)+cos(x))^2-2sin(x)cos(x)
Q23, 58:00, (1+tan^2(x))/(1+cot^2(x))
Q24, 1:02:20, (sec(x)-cos(x))/tan(x)
Q25, 1:03:34, sin(x)(csc(x)-sin(x))
Q26, 1:04:46, sin(x)/(1+cos(x))+(1+cos(x))/sin(x)
Q27, 1:07:29, (tan(x)+sec(x))(tan(x)-sec(x))
Q28, 1:10:16, cot(x+y)
Q29, 1:15:06, sin(pi/2-x)/cos(pi/2-x)
Q30, 1:16:08, cos(pi/2+x)
Q31, 1:23:00, cos(x+y)cos(x-y)
Q32, 1:27:55, sin(x+y)sin(x-y)
Q33, 1:31:21, sec(x+pi)/csc(x+pi/2)
Q34, 1:37:02, tan(x)tan(pi/2-x)
Q35, 1:37:33, sin(arcsec(x))
Q36, 1:39:45, tan(arccos(x))
Q37, 1:41:40, sec^2(arctan(x))
Q38, 1:45:17, cos(arctan(x/3))
Q39, 1:46:53, 2tan(x)/(1+tan^2(x))
Q40, 1:48:54, csc(x)sec(x)
Q41, 1:50:54, sin(x+pi/3)
Q42, 1:52:56, tan^2(x)/(csc(x)sec^3(x))
Q43, 1:54:53, 2tan(x)/(1-tan^2(x))
Q44, 1:57:14, tan(2arctan(x))
Q45, 1:59:47, cos(2arcsin(x))
Q46, 2:01:39, sin^2(x+pi/4)+sin^2(x-pi/4)
Q47, 2:10:21, sec(arctan(sin(x)))
Q48, 2:12:39, sin(x)+cos(x)
Q49, 2:16:10, sqrt(3)sin(x)-cos(x)
Q50, 2:19:05, (sin(x)+sin(y))/(cos(x)+cos(y))
Q51, 2:25:38, tan(3x)-tan(2x)-tan(x)
Q52, 2:28:46, (cos(x)-cos^3(x))/sin^2(x)
Q53, 2:29:50, cos(x+pi)
Q54, 2:31:45, sin(3x)
Q55, 2:34:13, cos(3x)
Q56, 2:35:50, sin(x)sin(y)
Q57, 2:39:10, cos(x)cos(y)
Q58, 2:41:03, sin(x)+sin(y)
Q59, 2:45:48, cos(x)+cos(y)
Q60, 2:48:02, 2cos^2(x)-cos(2x)
Q61, 2:48:47, cos(4x)
Q62, 2:51:52, sin(2x)cos(5x)
Q63, 2:55:58, sin^6(x)+cos^6(x)
Q64, 3:02:56, (sin(x)+sin(3x)+sin(5x))/(cos(x)+cos(3x)+cos(5x))
Q65, 3:08:50, (sin(3x)-sin(x))/(cos(3x)+cos(x))
Q66, 3:12:07, (1-cos(x))/(1+cos(x))
Q67, 3:15:08, cos^4(x)-sin^4(x)
Q68, 3:16:51, sqrt(1-sin(2x))
Q69, 3:19:44, cos(x)-sin(x)
Q70, 3:21:34, 2sec^2(x)/(4+4tan^2(x))^3
Q71, 3:23:24, sqrt(4-4sin^2(x))
Q72, 3:25:22, sin(2arccos(x))
Q73, 3:30:22, cos(2arctan(x))
Q74, 3:33:23, sec^2(x)+csc^2(x)
Q75, 3:35:44, tan(x)+tan(y)
Q76, 3:37:28, arctan(x)+arctan(y)
Q77, 3:41:04, cos(arcsin(x)+arcsin(y))
Q78, 3:43:25, cos^2(x)sin^2(x)
Q79, 3:48:56, (1-cos(x)+sin(x))/(1+cos(x)+sin(x))
Q80, 3:54:45, sin^4(x)
Q81, 4:01:52, (1+sin(2x))/cos(2x)
Q82, 4:04:58, (sin(x)+cos(x))^2+(sin(x)-cos(x))^2
Q83, 4:06:33, csc(2x)+cot(2x)
Q84, 4:08:02, (sin(x)+cos(x))/(csc(x)+sec(x))
Q85, 4:10:46, sin(5x)+sin(3x)
Q86, 4:11:56, cos(2x)cos(5x)
Q87, 4:13:51, sin^4(x)+cos^4(x)
Q88, 4:16:08, tan(x+pi/4)
Q89, 4:17:59, tan(x+pi/2)
Q90, 4:23:07, sin(arcsin(x)+arccos(y))
Q91, 4:24:50, Integral Ready Form: sin^5(x)
Q92, 4:28:24, Integral Ready Form: tan^3(x)sec(x)
Q93, 4:30:35, Integral Ready Form: tan^3(x)/sec(x)
Q94, 4:33:53, Integral Ready Form: sin^3(x)cos^3(x)
Q95, 4:35:27, Integral Ready Form: cos^2(x)/cot^3(x)
Q96, 4:38:07, Integral Ready Form: sec^6(x)
Q97, 4:40:13, Integral Ready Form: cot^5(x)
Q98, 4:42:45, Integral Ready Form: 1/(1+sin^2(x))
Q99, 4:47:00, Integral Ready Form: sec(x)
Q101, 4:49:00, (Bonus): sin(x)+sin(y)+sin(z) when x+y+z=pi
More about the "integral-ready forms" https://www.youtube.com/watch?v=UkOnnXvTADM&t=5s Receive SMS online on sms24.me
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