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Byju's Answer
Standard IX
Mathematics
Relationship between Trigonometric Ratios
If tanθ +1t...
Question
If
tan
θ
+
1
tan
θ
=
2
, then show that
tan
2
θ
+
1
tan
2
θ
=
2
.
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Solution
tan
θ
+
1
tan
θ
=
2
(
tan
θ
+
1
tan
θ
)
2
=
4
tan
2
θ
+
1
tan
2
θ
+
2
=
4
tan
2
θ
+
1
tan
2
θ
=
2
Hence proved.
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Similar questions
Q.
If
t
a
n
Θ
+
1
t
a
n
Θ
=
2
,
then the value of
t
a
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+
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t
a
n
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Q.
Let
tan
θ
+
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θ
=
m
and
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θ
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θ
=
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then show that
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.
Q.
Prave that:
(1)
sin
2
θ
cosθ
+
cosθ
=
secθ
(2)
cos
2
θ
1
+
tan
2
θ
=
1
(3)
1
-
sinθ
1
+
sinθ
=
secθ
-
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+
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=
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(5)
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+
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secθ
(6)
1
secθ
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sec
4
θ
-
cos
4
θ
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1
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2
cos
2
θ
(8)
secθ
+
tanθ
=
cos
θ
1
-
sinθ
(9) If
t
anθ
+
1
tanθ
=
2
, then show that
tan
2
θ
+
1
tan
2
θ
=
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(10)
tanA
1
+
tan
2
A
2
+
cotA
1
+
cot
2
A
2
=
sin
A
cos
A
(11)
sec
4
A
1
-
sin
4
A
-
2
tan
2
A
=
1
(12)
tanθ
secθ
-
1
=
tanθ
+
secθ
+
1
tanθ
+
secθ
-
1
Q.
If
t
a
n
θ
+
c
o
t
θ
=
2
,
then
t
a
n
2
θ
+
c
o
t
2
θ
= _____.
Q.
If
tan
θ
=
1
2
and
tan
ϕ
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tan
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θ
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is equal to
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