if 1/sec∅-1/tan∅-1/cos∅=sec∅xk,0°<ø<90°,then k=?
Answers
Answered by
0
Answer:
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
.
Explanation:
DO IT BY THIS METHOD
Similar questions
Geography,
4 months ago
English,
4 months ago
Chemistry,
9 months ago
Political Science,
11 months ago
Chemistry,
11 months ago