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Other
Quantitative Aptitude
Functions
Transform the...
Question
Transform the following expression
t
a
n
α
+
t
a
n
β
c
o
t
α
+
c
o
t
β
+
[
c
o
s
(
α
−
β
)
s
e
c
(
α
+
β
)
+
1
]
−
1
.
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Solution
t
a
n
α
+
t
a
n
β
c
o
t
α
+
c
o
t
β
+
[
c
o
s
(
α
−
β
)
s
e
c
(
α
+
β
)
+
1
]
−
1
=
t
a
n
α
+
t
a
n
β
t
a
n
β
+
t
a
n
α
t
a
n
α
.
t
a
n
β
+
1
c
o
s
(
α
−
β
)
c
o
s
(
α
+
β
)
+
1
=
t
a
n
α
t
a
n
β
+
c
o
s
(
α
+
β
)
c
o
s
(
α
−
β
)
+
c
o
s
(
α
+
β
)
=
t
a
n
α
.
t
a
n
β
+
c
o
s
α
c
o
s
β
−
s
i
n
α
s
i
n
β
2
c
o
s
α
c
o
s
β
=
t
a
n
α
t
a
n
β
+
1
2
−
t
a
n
α
t
a
n
β
2
=
1
2
+
t
a
n
α
t
a
n
β
2
=
1
+
t
a
n
α
t
a
n
β
2
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0
Similar questions
Q.
If
c
o
t
α
+
t
a
n
α
=
m
and
1
c
o
s
α
−
c
o
s
α
=
n
, then
Q.
tan
α
−
β
2
=
±
√
1
−
cos
(
α
−
β
)
1
+
cos
(
α
−
β
)
Q.
Identity transformations of Trigonometric Expressions.
prove the following identities.
1
+
t
a
n
α
+
t
a
n
2
α
1
+
c
o
t
α
+
c
o
t
2
α
=
t
a
n
2
α
.
Q.
If
cos
α
=
3
cos
β
−
1
3
−
cos
β
where
0
<
β
<
α
<
π
, then the value of
tan
α
2
t
a
n
β
2
=
Q.
If
t
a
n
α
=
m
m
+
1
and
t
a
n
β
=
1
1
+
2
m
then
t
a
n
(
α
+
β
)
equals-
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