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Byju's Answer
Standard XII
Mathematics
Determinant
Prove that if...
Question
Prove that if
α
,
β
, and
γ
are angles of a triangle, then sin
α
×
s
i
n
β
−
c
o
s
γ
=
c
o
s
α
c
o
s
β
Open in App
Solution
α
+
β
+
γ
=
π
⟹
γ
=
π
−
(
α
+
β
)
L
H
S
=
sin
α
sin
β
−
cos
γ
=
sin
α
sin
β
−
cos
(
π
−
(
α
+
β
)
)
=
sin
α
sin
β
+
cos
(
α
+
β
)
=
sin
α
sin
β
+
cos
α
cos
β
−
sin
α
sin
β
=
cos
α
cos
β
=
R
H
S
Suggest Corrections
0
Similar questions
Q.
cos
(
α
−
β
)
+
cos
(
β
−
γ
)
+
cos
(
γ
−
α
)
=
−
3
2
then prove that
cos
α
+
cos
β
+
cos
γ
=
sin
α
+
sin
β
+
sin
γ
=
0
Q.
If
c
o
s
α
+
c
o
s
β
+
c
o
s
γ
=
s
i
n
α
+
s
i
n
β
+
s
i
n
γ
=
0
, then
c
o
s
(
β
+
γ
)
+
c
o
s
(
γ
+
α
)
+
c
o
s
(
α
+
β
)
=
0
s
i
n
(
β
+
γ
)
s
i
n
(
γ
+
α
)
+
s
i
n
(
α
+
β
)
=
0
Q.
Assertion :The minimum value of the expression
sin
α
+
sin
β
+
sin
γ
where
α
,
β
,
γ
are real numbers such that
α
+
β
+
γ
=
π
is negative. Reason: If
α
+
β
+
γ
=
π
,then
α
,
β
,
γ
are the angles of a triangle.
Q.
If
cos
α
+
cos
β
+
cos
γ
=
0
=
sin
α
+
sin
β
+
sin
γ
=
0
then
cos
(
2
α
−
β
−
γ
)
+
cos
(
2
β
−
γ
−
α
)
+
cos
(
2
γ
−
α
−
β
)
=
Q.
Assertion :The minimum value of the expression
sin
α
+
sin
β
+
sin
γ
where
α
,
β
,
γ
are real number such that
α
+
β
+
γ
=
π
, is negative because- Reason:
α
,
β
,
γ
are angles of a triangle.
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