12 x1 t05 06 general solutions (2012)
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Transcript of 12 x1 t05 06 general solutions (2012)
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General Solutions of Trig Equations
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General Solutions of Trig Equations
xsin
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General Solutions of Trig Equations
xsin0x
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General Solutions of Trig Equations
xsin0x
x1sinx1sin
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General Solutions of Trig Equations
xsin0x
x1sinx1sin
xx 11 sinor sin
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General Solutions of Trig Equations
xsin0x
x1sinx1sin
xx 11 sinor sin
0x
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General Solutions of Trig Equations
xsin0x
x1sinx1sin
xx 11 sinor sin
0x
x1sin x1sin
![Page 8: 12 x1 t05 06 general solutions (2012)](https://reader030.fdocuments.in/reader030/viewer/2022032616/55a60d451a28abd77b8b48f1/html5/thumbnails/8.jpg)
General Solutions of Trig Equations
xsin0x
x1sinx1sin
xx 11 sinor sin
0x
x1sin x1sin
xx 11 sin2or sin
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General Solutions of Trig Equations
xsin0x
x1sinx1sin
xx 11 sinor sin
0x
x1sin x1sin
xx 11 sin2or sin xx 11 sin2or sin
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General Solutions of Trig Equations
xsin0x
x1sinx1sin
xx 11 sinor sin
0x
x1sin x1sin
xx 11 sin2or sin xx 11 sin2or sin
xsin xk k 1sin1 where k is an integer
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xcos
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xcos0x
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xcos0x
x1cos
x1cos
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xcos0x
x1cos
x1cos
xx 11 cos2or cos
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xcos0x
x1cos
x1cos
xx 11 cos2or cos
0x
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xcos0x
x1cos
x1cos
xx 11 cos2or cos
0x
x1cos x1cos
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xcos0x
x1cos
x1cos
xx 11 cos2or cos
0x
x1cos x1cos
xx 11 cosor cos
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xcos0x
x1cos
x1cos
xx 11 cos2or cos
0x
x1cos x1cos
xx 11 cosor cos
xx
xx11
11
cos2or coscosor cos
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xcos0x
x1cos
x1cos
xx 11 cos2or cos
0x
x1cos x1cos
xx 11 cosor cos
xx
xx11
11
cos2or coscosor cos
xcosxk 1cos2 where k is an integer
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xtan
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xtan0x
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xtan0x
x1tan
x1tan
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xtan0x
x1tan
x1tan
xx 11 tanor tan
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xtan0x
x1tan
x1tan
xx 11 tanor tan
0x
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xtan0x
x1tan
x1tan
xx 11 tanor tan
0x
x1tan x1tan
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xtan0x
x1tan
x1tan
xx 11 tanor tan
0x
x1tan x1tan
xx 11 tan2or tan
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xtan0x
x1tan
x1tan
xx 11 tanor tan
0x
x1tan x1tan
xx 11 tan2or tan
xx 11 tan2or tan
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xtan0x
x1tan
x1tan
xx 11 tanor tan
0x
x1tan x1tan
xx 11 tan2or tan
xx 11 tan2or tan
xtanxk 1tan where k is an integer
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23sin e.g. i
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23sin e.g. i
23sin1 1kk
where k is an integer
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23sin e.g. i
23sin1 1kk
where k is an integer
3
1 kk
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23sin e.g. i
23sin1 1kk
where k is an integer
3
1 kk
20If
32,
3
3,
3
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23sin e.g. i
23sin1 1kk
where k is an integer
3
1 kk
20If
32,
3
3,
3
2
1cos ii
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23sin e.g. i
23sin1 1kk
where k is an integer
3
1 kk
20If
32,
3
3,
3
2
1cos ii
21cos2 1k
where k is an integer
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23sin e.g. i
23sin1 1kk
where k is an integer
3
1 kk
20If
32,
3
3,
3
2
1cos ii
21cos2 1k
where k is an integer
432 k
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23sin e.g. i
23sin1 1kk
where k is an integer
3
1 kk
20If
32,
3
3,
3
2
1cos ii
21cos2 1k
where k is an integer
432 k
20If
45,
43
432,
43
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3
1tan iii
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3
1tan iii
31tan 1k
where k is an integer
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3
1tan iii
31tan 1k
where k is an integer
6 k
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3
1tan iii
31tan 1k
where k is an integer
6 k
20If
67,
6
6,
6
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3
1tan iii
31tan 1k
where k is an integer
6 k
20If
67,
6
6,
6
7
5sinsin iv
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3
1tan iii
31tan 1k
where k is an integer
6 k
20If
67,
6
6,
6
7
5sinsin iv
7
5sinsin1 1 kk
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3
1tan iii
31tan 1k
where k is an integer
6 k
20If
67,
6
6,
6
7
5sinsin iv
7
5sinsin1 1 kk
where k is an integer
7
21 kk
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3
1tan iii
31tan 1k
where k is an integer
6 k
20If
67,
6
6,
6
7
5sinsin iv
7
5sinsin1 1 kk
where k is an integer
7
21 kk
9
cos2cos xv
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3
1tan iii
31tan 1k
where k is an integer
6 k
20If
67,
6
6,
6
7
5sinsin iv
7
5sinsin1 1 kk
where k is an integer
7
21 kk
9
cos2cos xv
9coscos22 1 kx
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3
1tan iii
31tan 1k
where k is an integer
6 k
20If
67,
6
6,
6
7
5sinsin iv
7
5sinsin1 1 kk
where k is an integer
7
21 kk
9
cos2cos xv
9coscos22 1 kx
922 kx
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3
1tan iii
31tan 1k
where k is an integer
6 k
20If
67,
6
6,
6
7
5sinsin iv
7
5sinsin1 1 kk
where k is an integer
7
21 kk
9
cos2cos xv
9coscos22 1 kx
922 kx
18 kx
where k is an integer
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Exercise 1F; 4 to 8 ace etc9 to 1112ac