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Byju's Answer
Standard XII
Mathematics
Solving Simultaneous Trigonometric Equations
If α +β -γ ...
Question
If
α
+
β
−
γ
=
π
, show that
sin
2
α
+
sin
2
β
−
sin
2
γ
=
2
sin
α
sin
β
cos
γ
.
Open in App
Solution
L.H.S.
=
sin
2
α
+
sin
2
β
−
sin
2
γ
=
sin
2
α
+
sin
(
β
+
γ
)
sin
(
β
−
γ
)
=
sin
2
α
+
sin
(
β
+
γ
)
sin
(
π
−
α
)
[
∵
α
+
β
−
γ
=
π
gives
β
−
γ
=
π
−
α
]
=
sin
2
α
+
sin
(
β
+
γ
)
sin
α
=
sin
α
[
sin
α
+
sin
(
β
+
γ
)
]
sin
α
[
sin
(
β
−
γ
)
+
sin
(
β
+
γ
)
]
[
∵
sin
α
=
sin
{
π
−
(
β
−
γ
)
}
=
sin
(
β
−
γ
)
]
=
sin
α
⋅
2
sin
β
cos
γ
=
2
sin
α
sin
β
cos
γ
.
Suggest Corrections
0
Similar questions
Q.
State whether the given statement is true or false
If
α
+
β
−
γ
=
π
,
then show that
sin
2
α
+
sin
2
β
−
sin
2
γ
=
2
sin
α
sin
β
cos
γ
.
Q.
If
α
+
β
+
γ
=
π
, then the value of
sin
2
α
+
sin
2
β
−
sin
2
γ
is equal to
Q.
If
α
+
β
−
γ
=
π
,
Find m if
sin
2
α
+
sin
2
β
−
sin
2
γ
=
m
sin
α
sin
β
cos
γ
Q.
If α + β − γ = π and sin
2
α +sin
2
β − sin
2
γ = λ sin α sin β cos γ, then write the value of λ.
Q.
sin
2
(
α
−
β
)
+
sin
2
(
β
−
γ
)
+
sin
2
(
γ
−
α
)
=
−
4
sin
(
α
−
β
)
sin
(
β
−
γ
)
sin
(
γ
−
α
)
.
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