If seco - cosece =
then =
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Step-by-step explanation:
Since
tan
(
θ
)
=
3
4
>
0
and
sin
(
θ
)
<
0
,
θ
is in quadrant 3 (since
tan
(
θ
)
>
0
iff
θ
is in quadrant 1 or 3 and
sin
(
θ
)
<
0
iff
θ
is in quadrant 3 or 4).
cos
(
θ
)
must then be negative.
Remember that
sin
2
(
θ
)
+
cos
2
(
θ
)
=
1
. Divide both sides by
cos
2
(
θ
)
to get
sin
2
(
θ
)
cos
2
(
θ
)
+
1
=
1
cos
2
(
θ
)
. Since
tan
(
θ
)
=
sin
(
θ
)
cos
(
θ
)
, this is simply
tan
2
(
θ
)
+
1
=
1
cos
2
(
θ
)
. Thus,
cos
2
(
θ
)
=
1
tan
2
(
θ
)
+
1
.
Since
tan
(
θ
)
=
3
4
,
cos
2
(
θ
)
=
1
(
3
4
)
2
+
1
=
16
25
. Since
cos
(
θ
)
is negative,
cos
(
θ
)
=
−
√
16
25
=
−
4
5..
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