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Byju's Answer
Standard XII
Mathematics
Arithmetic Mean
If cos ( al...
Question
If cos (α + β) sin (γ + δ) = cos (α − β) sin (γ − δ), prove that cot α cot β cot γ = cot δ
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Solution
cos
α
+
β
sin
γ
+
δ
=
cos
α
-
β
sin
γ
-
δ
⇒
cos
α
cos
β
-
sin
α
sin
β
sin
γ
cos
δ
+
cos
γ
sin
δ
=
cos
α
cos
β
+
sin
α
sin
β
sin
γ
cos
δ
-
cos
γ
sin
δ
Dividing
both
sides
by
sin
α
sin
β
sin
γ
sin
δ
:
cos
α
cos
β
-
sin
α
sin
β
sin
γ
cos
δ
+
cos
γ
sin
δ
sin
α
sin
β
sin
γ
sin
δ
=
cos
α
cos
β
+
sin
α
sin
β
sin
γ
cos
δ
-
cos
γ
sin
δ
sin
α
sin
β
sin
γ
sin
δ
⇒
cos
α
cos
β
-
sin
α
sin
β
sin
α
sin
β
×
sin
γ
cos
δ
+
cos
γ
sin
δ
sin
γ
sin
δ
=
cos
α
cos
β
+
sin
α
sin
β
sin
α
sin
β
×
sin
γ
cos
δ
-
cos
γ
sin
δ
sin
γ
sin
δ
⇒
cot
α
cot
β
-
1
cot
δ
+
cot
γ
=
cot
α
cot
β
+
1
cot
δ
-
cot
γ
⇒
cot
α
cot
β
c
o
t
δ
+
cot
α
cot
β
c
o
t
γ
-
c
o
t
δ
-
c
o
t
γ
=
cot
α
cot
β
c
o
t
δ
-
cot
α
cot
β
c
o
t
γ
+
c
o
t
δ
-
c
o
t
γ
⇒
-
cot
δ
-
cot
δ
=
-
cot
α
cot
β
cot
γ
-
cot
α
cot
β
cot
γ
⇒
-
2
cot
δ
=
-
2
cot
α
cot
β
cot
γ
⇒
cot
α
cot
β
cot
γ
=
cot
δ
Hence
proved
.
Suggest Corrections
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Q.
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If
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are the roots of
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Δ
=
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∣ ∣ ∣
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)
and
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γ
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β
)
taken in order, where
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Q.
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2
+
q
x
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=
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show that
q
2
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p
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(
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(
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+
δ
)
(
β
+
δ
)
=
0
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