450
22
2
tan u
cot u
4
tanu
cot u
+=
+
−
22
tan u
cot u
4
2
+=
+
22
tan u
cot u
6
+=
6.
tan r
2sen r
=
sen r
2sen r
cos r
=
sen r
2 sen r
=
cos r
1 2 cos r
=
1
cos r
2
=
Por defnición en el círculo trigonométrico:
x1
=
,
h2
=
y
222
1y2
y
3
+=
⇒
=
Así
3
senr
2
=
y
3
tanr
3
1
=
=
por lo que
33 3
senr tanr
21 2
=
=
7.
tan A cot A
sec A csc A
+= ⋅
sen A
cos A
sec A csc A
cos A
sen A
+=
⋅
22
sen A cos A
sec A csc A
sen Acos A
+
=
⋅
1
sec A csc A
sen Acos A
=
⋅
11
sec A csc A
sen A cos A
⋅=⋅
csc A sec A
sec A csc A
⋅= ⋅
(Se verifca la igualdad inicial)
8.
22
2
cos u
sen u 1 2sen u
−=
−
( )
22
2
1 sen u
sen u 1 2sen u
−
−=
−
22
2
1 sen u
sen u 1 2sen u
−−=
−
22
1 2sen u 1 2sen u
−=
−
(Se verifca la igualdad inicial)
9.
22
csc
sec
csc
sec
sen
cos
θθ
θθ
θθ
+=⋅
22
csc cos
sen sec
csc
sec
sen cos
θθ
θθ
θθ
θθ
+
=
⋅
22
11
cos
sen
sen
cos
csc
sec
sen cos
θθ
θθ
θθ
θθ
+
=
⋅
22
cos
sen
sen
cos
csc
sec
sen cos
θθ
θθ
θθ
θθ
+
=
⋅
22
22
cos
sen
sen cos
csc
sec
sen cos
θθ
θθ
θθ
θθ
+
=
⋅
22
1
sen cos
csc
sec
sen cos
1
θθ
θθ
θθ
=
⋅
22
22
1
csc
sec
sen
cos
θθ
θθ
=
⋅
22
22
11
csc
sec
sen
cos
θθ
θθ
⋅=
⋅
22
22
11
csc
sec
sen
cos
θθ
θθ
⋅=
⋅
( ) ( )
22
22
csc
sec
csc
sec
θ
θ
θθ
⋅=
⋅
22
22
csc
sec
csc
sec
θθ
θθ
⋅=⋅
(Se verifca la igualdad inicial)
Apéndice 1