How to verify or prove trigonometric identities? I put the problems in the multiple-choice format so the problems are more challenging. Moreover, we will also derive the triple-angle identity, the quadruple-angle identity for cosine, i.e. cos(3x) and cos(4x), and the power reduction identity for sin^4(x). Mastering these problems will prepare you for your calculus class, especially when we do derivatives and integrals.
#trigonometry #math #precalculus
File 👉 https://www.patreon.com/posts/24-trig-identity-88803595
Solutions 👉 https://www.patreon.com/posts/my-hand-written-88804184
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Thanks to @takureido3122 & @sohampinemath1086 for the time stamps!!!
Intro - 00:00
1 - 00:51 — sinx+cotxcosx
2 - 04:40 — (secx-cosx)/sinx
3 - 07:16 — cotx/(cscx-sinx)
4 - 09:00 — (1+2cosx)/(2+secx)
5 - 10:45 — 1/(1-sinx)+1/(1+sinx)
6 - 13:00 — (2+cot²x)/csc²x-1
7 - 15:36 — tan(x+π/4)
8 - 19:11 — cos(3x)
9 - 24:09 — cos(4x)
10 - 29:32 — sec(sin^-1x)
11 - 32:42 — cos(2tan^-1x)
12 - 36:56 — tan(2sin^-1x)
13 - 42:44 — csc²x+sec²x
14 - 45:41 — cosx cos(2x)
15 - 49:38 — sin⁴x
16 - 57:22 — sin⁴x-cos⁴x
17 - 1:02:04 — tanx+tany
18 - 1:04:47 — 2tanx/(1+tan²x)
19 - 1:07:25 — 1/(secx-1)+1/(secx+1)
20 - 1:12:08 — (sinx+tanx)/(1+cos(-x))
21 - 1:16:14 — cos²x-sin⁴x sec²x
22 - 1:14:50 — (sinx+cosx)²
23 - 1:20:18 — sinx/(1-cotx)+cosx/(1+tanx)
24 - 1:23:57 — sec²(x/2)
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