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Byju's Answer
Standard XIII
Mathematics
Allied Angles
If θ=178°, th...
Question
If
θ
=
178
°
, then the value of
sin
θ
√
1
+
cot
2
θ
+
cos
θ
√
1
+
tan
2
θ
is
A
2
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B
−
2
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C
0
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D
1
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Solution
The correct option is
C
0
Given expression
sin
θ
|
cosec
θ
|
+
cos
θ
|
sec
θ
|
=
sin
θ
cosec
θ
+
cos
θ
(
−
sec
θ
)
(
∵
θ
∈
Q
2
∴
cosec
θ
>
0
,
sec
θ
<
0
)
=
1
−
1
=
0
Suggest Corrections
0
Similar questions
Q.
Prove that
sin
θ
−
cos
θ
+
1
sin
θ
+
cos
θ
−
1
=
1
sec
θ
−
tan
θ
, using the identity
sec
2
θ
=
1
+
tan
2
θ
.
Q.
Prove the following.
(1) secθ (1 – sinθ) (secθ + tanθ) = 1
(2) (secθ + tanθ) (1 – sinθ) = cosθ
(3) sec
2
θ + cosec
2
θ = sec
2
θ × cosec
2
θ
(4) cot
2
θ – tan
2
θ = cosec
2
θ – sec
2
θ
(5) tan
4
θ + tan
2
θ = sec
4
θ – sec
2
θ
(6)
1
1
-
sin
θ
+
1
1
+
sin
θ
=
2
sec
2
θ
(7) sec
6
x
– tan
6
x
= 1 + 3sec
2
x
× tan
2
x
(8)
tan
θ
s
e
c
θ
+
1
=
s
e
c
θ
-
1
tan
θ
(9)
tan
3
θ
-
1
tan
θ
-
1
=
sec
2
θ
+
tan
θ
(10)
sin
θ
-
cos
θ
+
1
sin
θ
+
cos
θ
-
1
=
1
sin
θ
-
tan
θ
Q.
IS LHS=RHS?
sin
θ
+
cos
θ
sin
θ
−
cos
θ
+
sin
θ
−
cos
θ
sin
θ
+
cos
θ
=
1
sin
2
θ
−
cos
2
θ
=
sec
2
θ
tan
2
θ
−
1
Say true or false.
Q.
If
cos
θ
=
1
2
then the value of
2
sec
θ
1
+
tan
2
θ
is
Q.
If
cot
2
θ
=
7
8
and
0
<
θ
<
90
o
, then the value of
(
1
+
sin
θ
)
(
1
−
sin
θ
)
(
1
+
cos
θ
)
(
1
−
cos
θ
)
is equal to :
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Standard XIII Mathematics
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