Question

Garmine whether the set of functions [1, tanx, secx] ava Ninaarly dependent or linearly independent Sol #2 July 2010 1 1 tanx secx x) = 0 sec'x secx tanx tanx secx W(x) = 0 sec²x secxtanx O 2secxtanx secx tan²x+sex 0 I seer kanx Secxtan'x + secx = (1) | sec2x secx tanx 2 secx tanx secxtan²x+sec³x W(1) = 1 1 0 1 0 ? 0 1 = sec²x [secx tan²x+sec²x] - 2 secx tan²x 1 0 = sec'x tan'x + secx - 2 sec³x tan²x = (1) 0 1 = secx - sec³x tan²x = (1) -0 = 1 ?0 = Sec³x [sec²x-tan2x] ? = sec3x [?] = sec3x ?0 1, tanx, secx) are Linearly independ 1+tan²x=5 *{1, tanx, secx) are Linearly indel

          Garmine whether the set of functions [1, tanx, secx]
ava Ninaarly dependent or linearly independent
Sol #2
July 2010
1
1
tanx
secx
x)
=
0
sec'x
secx tanx
tanx
secx
W(x) =
0
sec²x
secxtanx
O 2secxtanx secx tan²x+sex
0
I seer kanx
Secxtan'x + secx
=
(1)
|
sec2x
secx tanx
2 secx tanx secxtan²x+sec³x
W(1) =
1
1
0
1
0
?
0
1
= sec²x [secx tan²x+sec²x] - 2 secx tan²x
1
0
=
sec'x tan'x + secx - 2 sec³x tan²x
=
(1)
0
1
=
secx - sec³x tan²x
=
(1) -0 = 1 ?0
= Sec³x [sec²x-tan2x]
?
= sec3x [?]
= sec3x ?0
1, tanx, secx) are Linearly independ
1+tan²x=5
*{1, tanx, secx) are Linearly indel

Garmine whether the set of functions [1, tanx, secx]
ava Ninaarly dependent or linearly independent
Sol #2
July 2010
1
1
tanx
secx
x)
=
0
sec'x
secx tanx
tanx
secx
W(x) =
0
sec²x
secxtanx
O 2secxtanx secx tan²x+sex
0
I seer kanx
Secxtan'x + secx
=
(1)
|
sec2x
secx tanx
2 secx tanx secxtan²x+sec³x
W(1) =
1
1
0
1
0
?
0
1
= sec²x [secx tan²x+sec²x] - 2 secx tan²x
1
0
=
sec'x tan'x + secx - 2 sec³x tan²x
=
(1)
0
1
=
secx - sec³x tan²x
=
(1) -0 = 1 ?0
= Sec³x [sec²x-tan2x]
?
= sec3x [?]
= sec3x ?0
1, tanx, secx) are Linearly independ
1+tan²x=5
*1, tanx, secx) are Linearly indel

Added by Pamela A.

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