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Byju's Answer
Standard XII
Mathematics
Composition of Trigonometric Functions and Inverse Trigonometric Functions
If α + tanα...
Question
If
(
sec
α
+
tan
α
)
(
sec
β
+
tan
β
)
(
sec
γ
+
tan
γ
)
=
tan
α
tan
β
tan
γ
, then
(
sec
α
−
tan
α
)
(
sec
β
−
tan
β
)
(
sec
γ
−
tan
γ
)
=
Open in App
Solution
Solution -
(
s
e
c
α
+
t
a
n
α
)
(
s
e
c
β
+
t
a
n
β
)
(
s
e
c
γ
+
t
a
n
γ
)
=
t
a
n
α
t
a
n
β
t
a
n
γ
__ (1)
Now,
Multiply
(
s
e
c
α
−
t
a
n
α
)
(
s
e
c
β
−
t
a
n
β
)
(
s
e
c
γ
−
t
a
n
γ
)
in both sides
1
=
t
a
n
α
t
a
n
β
t
a
n
γ
(
s
e
c
α
−
t
a
n
α
)
(
s
e
c
β
−
t
a
n
β
)
(
s
e
c
γ
−
t
a
n
γ
)
Because
s
e
c
2
θ
−
t
a
n
2
θ
=
1
(
s
e
c
α
−
t
a
n
α
)
(
s
e
c
β
−
t
a
n
β
)
(
s
e
c
γ
−
t
a
n
γ
)
=
1
t
a
n
α
t
a
n
β
.
t
a
n
γ
=
c
o
t
α
c
o
t
β
c
o
t
γ
.
Suggest Corrections
0
Similar questions
Q.
Prove that
tan
α
+
tan
β
+
tan
γ
−
tan
α
tan
β
tan
γ
=
sin
(
α
+
β
+
γ
)
cos
α
cos
β
cos
γ
Q.
I
f
α
+
β
=
π
2
a
n
d
β
+
γ
=
α
,
t
h
e
n
t
a
n
α
e
q
u
a
l
s
Q.
If
0
<
α
<
β
<
γ
<
π
/
2
, then show
tan
α
<
sin
α
+
sin
β
+
sin
γ
cos
α
+
cos
β
+
cos
γ
<
tan
γ
Q.
If
α
,
β
,
γ
ϵ
[
0
,
2
π
]
, then sum of all positive values of
α
,
β
,
γ
if,
sin
α
=
−
1
√
2
,
cos
β
=
−
1
2
,
tan
γ
=
−
√
3
, is
Q.
If
α
,
β
,
γ
∈
[
0
,
2
π
]
, then the sum of all possible values of
α
,
β
,
γ
if
sin
α
=
−
1
√
2
,
cos
β
=
−
1
2
,
tan
γ
=
−
√
3
, is
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