Description: Double-angle formula for cosine in terms of sine. (Contributed by NM, 12-Sep-2008)
Ref | Expression | ||
---|---|---|---|
Assertion | cos2tsin | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cos2t | |
|
2 | 2cn | |
|
3 | sincl | |
|
4 | 3 | sqcld | |
5 | coscl | |
|
6 | 5 | sqcld | |
7 | adddi | |
|
8 | 2 4 6 7 | mp3an2i | |
9 | sincossq | |
|
10 | 9 | oveq2d | |
11 | 8 10 | eqtr3d | |
12 | 2t1e2 | |
|
13 | 11 12 | eqtrdi | |
14 | mulcl | |
|
15 | 2 4 14 | sylancr | |
16 | mulcl | |
|
17 | 2 6 16 | sylancr | |
18 | subadd | |
|
19 | 2 15 17 18 | mp3an2i | |
20 | 13 19 | mpbird | |
21 | 20 | oveq1d | |
22 | ax-1cn | |
|
23 | sub32 | |
|
24 | 2 22 23 | mp3an13 | |
25 | 15 24 | syl | |
26 | 2m1e1 | |
|
27 | 26 | oveq1i | |
28 | 25 27 | eqtrdi | |
29 | 1 21 28 | 3eqtr2d | |