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Byju's Answer
Standard X
Mathematics
Trigonometric Identity- 3
If coθ+θ=P,...
Question
If
c
o
sec
θ
+
cot
θ
=
P
, then find
cos
θ
in terms of
P
.
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Solution
We know the trignometric identity
c
o
s
e
c
2
θ
−
c
o
t
2
θ
=
1
which is written as
(
c
o
s
e
c
θ
−
c
o
t
θ
)
(
c
o
s
e
c
θ
+
c
o
s
θ
)
=
1
Given
c
o
s
e
c
θ
+
c
o
s
θ
=
P
(
1
)
, hence
c
o
s
e
c
θ
−
c
o
s
θ
=
1
P
(
2
)
. By adding (1) and (2), we obtain
2
c
o
s
e
c
θ
=
P
+
1
P
=
P
2
+
1
P
Hence
s
i
n
θ
=
2
P
P
2
+
1
and
s
i
n
2
θ
=
4
P
2
(
P
2
+
1
)
2
c
o
s
2
θ
=
1
−
s
i
n
2
θ
=
1
−
4
P
2
(
P
2
+
1
)
2
=
(
P
2
−
1
)
2
(
P
2
+
1
)
2
c
o
s
θ
=
P
2
−
1
P
2
+
1
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