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Byju's Answer
Standard XII
Mathematics
Sin(A+B)Sin(A-B)
If α+β =π 2...
Question
If
(
α
+
β
)
=
π
2
and
(
β
+
γ
)
=
α
, then
t
a
n
α
equals
A
2
(
t
a
n
β
+
t
a
n
γ
)
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B
t
a
n
β
+
t
a
n
γ
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C
t
a
n
β
+
2
t
a
n
γ
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D
2
t
a
n
β
+
t
a
n
γ
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Solution
The correct option is
C
t
a
n
β
+
2
t
a
n
γ
α
+
β
=
π
2
⇒
α
=
π
2
−
β
⇒
t
a
n
α
=
c
o
t
β
⇒
t
a
n
α
t
a
n
β
=
1
Next,
β
+
γ
=
α
⇒
α
−
β
=
γ
⇒
t
a
n
α
−
t
a
n
β
1
+
t
a
n
α
t
a
n
β
=
t
a
n
γ
⇒
t
a
n
α
−
t
a
n
β
=
2
t
a
n
γ
⇒
t
a
n
α
=
t
a
n
β
+
2
t
a
n
γ
.
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0
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Q.
If
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then
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+
β
+
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=
Q.
If
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β
=
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α
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γ
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α
+
γ
)
, then
tan
α
,
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β
,
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are in which series where
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a
n
d
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β
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Q.
If
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=
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sin
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α
+
γ
)
show that
tan
α
,
tan
β
,
tan
γ
are in H.P. where
α
≠
0
a
n
d
γ
≠
0
a
n
d
β
≠
π
2
Q.
Prove that
tan
α
+
tan
β
+
tan
γ
−
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