(secA + cosecA)^2=(1+tanA)^2+(1+cotA)^2
Answers
Step-by-step explanation:
Hence, the values ofA satisfying the equation
(
1
+
tan
A
)
2
+
(
1
+
cot
A
)
2
=
(
sec
A
+
csc
A
)
2
are,
A
=
...
...
,
−
7
π
2
,
−
3
π
,
−
5
π
2
,
−
2
π
,
−
3
π
2
,
−
π
,
−
π
2
,
0
,
π
2
,
π
,
3
π
2
,
2
π
,
5
π
2
,
3
π
,
7
π
2
,
...
...
Explanation:
(
1
+
tan
A
)
2
+
(
1
+
cot
A
)
2
=
(
sec
A
+
csc
A
)
2
tan
A
=
sin
A
cos
A
cot
A
=
cos
A
sin
A
sec
A
=
1
cos
A
csc
A
=
1
sin
A
(
1
+
sin
A
cos
A
)
2
+
(
1
+
cos
A
sin
A
)
2
=
(
1
cos
A
+
1
sin
A
)
2
(
cos
A
+
sin
A
)
2
cos
2
A
+
(
sin
A
+
cos
A
)
2
sin
2
A
=
(
sin
A
+
cos
A
)
2
sin
A
cos
A
(
cos
A
+
sin
A
)
2
(
1
cos
2
A
+
1
sin
2
A
)
=
(
cos
A
+
sin
A
)
2
(
1
sin
A
cos
A
)
sin
2
A
+
cos
2
A
sin
2
A
cos
2
A
=
1
sin
A
cos
A
1
(
sin
A
cos
A
)
2
=
1
sin
A
cos
A
(
sin
A
cos
A
)
2
=
sin
A
cos
A
(
sin
A
cos
A
)
2
−
sin
A
cos
A
=
0
sin
A
cos
A
(
sin
A
cos
A
−
1
)
=
0
sin
A
=
0
,
cos
A
=
0
,
sin
A
cos
A
−
1
=
0
sin
A
=
0
→
A
=
0
,
π
,
2
π
,
3
π
,
...
cos
A
=
0
→
A
=
π
2
,
3
π
2
,
5
π
2
,
7
π
2
,
...
...
sin
A
cos
A
=
0
→
1
2
sin
2
A
=
0
→
sin
2
A
=
0
2
A
=
0
,
π
,
2
π
,
3
π
,
...
A
=
0
,
π
2
,
π
,
3
π
2
,
2
π
,
5
π
2
,
3
π
,
7
π
2
,
...
...
Hence, the values ofA satisfying the equation
(
1
+
tan
A
)
2
+
(
1
+
cot
A
)
2
=
(
sec
A
+
csc
A
)
2
are,
A
=
...
...
,
−
7
π
2
,
−
3
π
,
−
5
π
2
,
−
2
π
,
−
3
π
2
,
−
π
,
−
π
2
,
0
,
π
2
,
π
,
3
π
2
,
2
π
,
5
π
2
,
3
π
,
7
π
2
,
...
...
Step-by-step explanation:
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