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Byju's Answer
Standard XII
Mathematics
Property 4
Find x from t...
Question
Find x from the following equations:
(
i
)
cosec
π
2
+
θ
+
x
cos
θ
cot
π
2
+
θ
=
sin
π
2
+
θ
(
ii
)
x
cot
π
2
+
θ
+
tan
π
2
+
θ
sin
θ
+
cosec
π
2
+
θ
=
0
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Solution
90
°
=
π
2
i
We
have
:
cosec
90
°
+
θ
+
x
cos
θ
cot
90
°
+
θ
=
sin
90
°
+
θ
⇒
sec
θ
+
x
cos
θ
-
tan
θ
=
cos
θ
⇒
sec
θ
-
x
cosθ
tanθ
=
cos
θ
⇒
sec
θ
-
x
cosθ
×
sin
θ
cos
θ
=
cos
θ
⇒
sec
θ
-
x
sin
θ
=
cos
θ
⇒
sec
θ
-
cos
θ
=
x
sin
θ
⇒
1
cos
θ
-
cosθ
=
x
sin
θ
⇒
1
-
cos
2
θ
cos
θ
=
x
sin
θ
⇒
sin
2
θ
cosθ
=
x
sin
θ
⇒
sin
2
θ
cos
θ
sin
θ
=
x
⇒
sin
θ
cos
θ
=
x
⇒
tan
θ
=
x
∴
x
=
tan
θ
ii
We
have
:
x
cot
90
°
+
θ
+
tan
90
°
+
θ
sin
θ
+
cosec
90
°
+
θ
=
0
⇒
x
-
tan
θ
+
-
cot
θ
sin
θ
+
sec
θ
=
0
⇒
-
x
tan
θ
-
cot
θ
sin
θ
+
sec
θ
=
0
⇒
-
x
×
sin
θ
cos
θ
-
cos
θ
sin
θ
×
sin
θ
+
1
cos
θ
=
0
⇒
-
x
×
sin
θ
cos
θ
-
cos
θ
+
1
cos
θ
=
0
⇒
-
x
sin
θ
-
cos
2
θ
+
1
cos
θ
=
0
⇒
-
x
sin
θ
-
cos
2
θ
+
1
=
0
⇒
-
x
sin
θ
+
sin
2
θ
=
0
⇒
x
sin
θ
=
sin
2
θ
⇒
x
=
sin
2
θ
sin
θ
⇒
x
=
sin
θ
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0
Similar questions
Q.
Find x from the following equations:
(i) cosec (90° + θ) + x cos θ cot (90° + θ) = sin (90° + θ)
(ii) x cot (90° + θ) + tan (90° + θ) sin θ + cosec (90° + θ) = 0
Q.
Find x:
x
cot
(
90
+
θ
)
+
tan
(
90
+
θ
)
s
i
n
θ
+
cos
e
c
(
90
+
θ
)
=
0
Q.
if
cos
θ
=
12
13
and
θ
∈
(
0
,
π
2
]
,
then
144
(
tan
(
−
θ
)
×
sec
(
−
θ
)
]
Q.
Prove that:
[
1
+
cot
θ
−
sec
(
θ
+
π
2
)
]
[
1
+
cot
θ
+
sec
(
θ
+
π
2
)
]
=
2
cot
θ
Q.
(
1
+
t
a
n
θ
+
c
o
t
θ
)
(
s
i
n
θ
−
c
o
s
θ
)
=
(
s
e
c
θ
c
o
s
e
c
2
θ
−
c
o
s
e
c
θ
s
e
c
2
θ
)
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