Step |
Hyp |
Ref |
Expression |
1 |
|
atancl |
|
2 |
|
cosval |
|
3 |
1 2
|
syl |
|
4 |
|
efiatan2 |
|
5 |
|
ax-icn |
|
6 |
|
mulneg12 |
|
7 |
5 1 6
|
sylancr |
|
8 |
|
atanneg |
|
9 |
8
|
oveq2d |
|
10 |
7 9
|
eqtr4d |
|
11 |
10
|
fveq2d |
|
12 |
|
atandmneg |
|
13 |
|
efiatan2 |
|
14 |
12 13
|
syl |
|
15 |
|
atandm4 |
|
16 |
15
|
simplbi |
|
17 |
|
mulneg2 |
|
18 |
5 16 17
|
sylancr |
|
19 |
18
|
oveq2d |
|
20 |
|
ax-1cn |
|
21 |
|
mulcl |
|
22 |
5 16 21
|
sylancr |
|
23 |
|
negsub |
|
24 |
20 22 23
|
sylancr |
|
25 |
19 24
|
eqtrd |
|
26 |
|
sqneg |
|
27 |
16 26
|
syl |
|
28 |
27
|
oveq2d |
|
29 |
28
|
fveq2d |
|
30 |
25 29
|
oveq12d |
|
31 |
11 14 30
|
3eqtrd |
|
32 |
4 31
|
oveq12d |
|
33 |
|
addcl |
|
34 |
20 22 33
|
sylancr |
|
35 |
|
subcl |
|
36 |
20 22 35
|
sylancr |
|
37 |
16
|
sqcld |
|
38 |
|
addcl |
|
39 |
20 37 38
|
sylancr |
|
40 |
39
|
sqrtcld |
|
41 |
39
|
sqsqrtd |
|
42 |
15
|
simprbi |
|
43 |
41 42
|
eqnetrd |
|
44 |
|
sqne0 |
|
45 |
40 44
|
syl |
|
46 |
43 45
|
mpbid |
|
47 |
34 36 40 46
|
divdird |
|
48 |
20
|
a1i |
|
49 |
48 22 48
|
ppncand |
|
50 |
|
df-2 |
|
51 |
49 50
|
eqtr4di |
|
52 |
51
|
oveq1d |
|
53 |
32 47 52
|
3eqtr2d |
|
54 |
53
|
oveq1d |
|
55 |
|
2cnd |
|
56 |
|
2ne0 |
|
57 |
56
|
a1i |
|
58 |
55 40 55 46 57
|
divdiv32d |
|
59 |
|
2div2e1 |
|
60 |
59
|
oveq1i |
|
61 |
58 60
|
eqtrdi |
|
62 |
3 54 61
|
3eqtrd |
|