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Byju's Answer
Standard XII
Mathematics
Differentiation Using Substitution
56. tan 4thet...
Question
56. tan 4theta tan 2theta = 1 then tan 3theta=? 1) 1 2)0 3)1/root3 4) root3
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Similar questions
Q.
If
tan
θ
1
,
tan
θ
2
,
tan
θ
3
,
tan
θ
4
are the roots of the equation
x
4
−
x
3
sin
2
β
+
x
2
cos
2
β
−
x
cos
β
−
sin
β
=
0
then
tan
(
θ
1
+
θ
2
+
θ
3
+
θ
4
)
=
Q.
The number of roots of
(
1
−
tan
θ
)
(
1
+
sin
2
θ
)
=
1
+
tan
θ
for
θ
∈
[
0
,
2
π
)
]
is:
Q.
If
tan
a
,
tan
b
,
tan
c
,
tan
d
are the roots of the eqn
tan
(
45
°
+
θ
)
=
3
tan
3
θ
, then
1
tan
a
+
1
tan
b
+
1
tan
c
+
1
tan
d
is
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
-
tanθ
(4)
secθ
-
cosθ
cotθ
+
tanθ
=
tanθ
secθ
(5)
cotθ
+
tanθ
=
cosecθ
secθ
(6)
1
secθ
-
tanθ
=
secθ
+
tanθ
(7)
sec
4
θ
-
cos
4
θ
=
1
-
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
=
2
(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
θ
=
30
∘
, verify that :
(i)
tan
2
θ
=
2
tan
θ
1
−
tan
2
θ
(ii)
tan
2
θ
=
4
tan
θ
1
+
tan
2
θ
(iii)
cos
2
θ
=
1
−
tan
2
θ
1
+
tan
2
θ
(iv)
cos
3
θ
=
4
cos
3
θ
−
3
cos
θ
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