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Byju's Answer
Standard IX
Mathematics
Relationship between Trigonometric Ratios
State whether...
Question
State whether the statement is true/false
tan
θ
1
−
cot
θ
+
cot
θ
1
−
tan
θ
=
sec
θ
cos
e
c
θ
.
A
True
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B
False
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Solution
The correct option is
B
False
tan
θ
1
−
cot
θ
+
cot
θ
1
−
tan
θ
=
sin
θ
cos
θ
1
−
cos
θ
sin
θ
+
cos
θ
sin
θ
1
−
sin
θ
cos
θ
=
sin
2
θ
cos
θ
(
sin
θ
−
cos
θ
)
−
cos
2
θ
sin
θ
(
sin
θ
−
cos
θ
)
=
1
sin
θ
−
cos
θ
(
sin
2
θ
cos
θ
−
cos
2
θ
sin
θ
)
=
sin
3
θ
−
cos
3
θ
(
sin
θ
−
cos
θ
)
sin
θ
cos
θ
=
(
sin
θ
−
cos
θ
)
(
sin
2
θ
+
cos
2
θ
+
sin
θ
cos
θ
)
(
sin
θ
−
cos
θ
)
sin
θ
cos
θ
(
∵
a
3
−
b
3
=
(
a
−
b
)
(
a
2
+
b
2
+
a
b
)
)
=
1
+
sin
θ
cos
θ
sin
θ
cos
θ
=
1
+
sec
θ
cosec
θ
So the relation is
False
Suggest Corrections
0
Similar questions
Q.
State whether the following statement is true/false
1
+
sec
θ
−
tan
θ
1
+
sec
θ
−
tan
θ
=
1
−
sin
θ
cos
θ
Q.
State whether true or false:
sec
θ
−
tan
θ
=
3
Then
sec
θ
+
tan
θ
=
−
3
Q.
State whether true or false
sec
θ
−
tan
θ
=
8
Then
sec
θ
+
tan
θ
=
1
8
Q.
tan
θ
1
−
cot
θ
+
cot
θ
1
−
tan
θ
−
sec
θ
c
o
s
e
c
θ
=
.
Q.
State whether the given statement is true or false
√
1
+
sin
θ
1
−
sin
θ
=
sec
θ
−
tan
θ
,
−
π
2
<
θ
<
π
2
.
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