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Byju's Answer
Standard XII
Mathematics
Standard Formulae - 3
If 0≤α , β≤...
Question
If
0
≤
α
,
β
≤
90
and
tan
(
α
+
β
)
=
3
and
tan
(
α
−
β
)
=
2
then value of
sin
2
α
is ?
Open in App
Solution
Here,
0
≤
α
,
β
≤
90
∘
⟹
1
s
t
Q
u
a
d
r
a
n
t
Let
A
=
α
+
β
a
n
d
B
=
α
−
β
A
+
B
=
2
α
Using
t
a
n
(
A
+
B
)
=
t
a
n
A
+
t
a
n
B
1
−
t
a
n
A
t
a
n
B
t
a
n
(
2
α
)
=
t
a
n
[
(
α
+
β
)
+
(
α
−
β
)
]
t
a
n
(
2
α
)
=
t
a
n
(
α
+
β
)
+
t
a
n
(
α
−
β
)
1
−
t
a
n
(
α
+
β
)
t
a
n
(
α
−
β
)
t
a
n
(
2
α
)
=
3
+
2
1
−
3
⋅
2
=
5
−
5
t
a
n
(
2
α
)
=
−
1
<
0
Now
,
0
≤
α
≤
90
0
≤
2
α
≤
180
⟹
1
s
t
o
r
2
n
d
Q
u
a
d
r
a
n
t
t
a
n
(
2
α
)
=
−
1
<
0
⟹
2
n
d
Q
u
a
d
r
a
n
t
2
α
=
π
−
π
4
s
i
n
(
2
α
)
=
s
i
n
(
π
−
π
4
)
=
s
i
n
π
4
s
i
n
(
2
α
)
=
1
√
2
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1
Similar questions
Q.
If
0
≤
α
,
β
≤
90
∘
and
t
a
n
(
α
+
β
)
=
3
and
t
a
n
(
α
−
β
)
=
2
, then the value of
s
i
n
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Q.
Prove that:
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If
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γ
)
t
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α
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β
+
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=
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γ
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Q.
If
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∘
and
β
=
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