Cos(x-y)=-1 , cos x + cos y
Answers
Answered by
1
Step-by-step explanation:
Answer:
cos
(
x
−
y
)
=
a
2
+
b
2
−
2
2
Explanation:
Using de Moivre's identity
e
i
ϕ
=
cos
ϕ
+
i
sin
ϕ
Adding term to term
(
i
sin
x
+
i
sin
y
=
i
a
cos
x
+
cos
y
=
b
)
giving
e
i
x
+
e
i
y
=
ρ
e
i
α
with
ρ
=
√
a
2
+
b
2
Adding now
(
−
i
sin
x
−
i
sin
y
=
−
i
a
cos
x
+
cos
y
=
b
)
e
−
i
x
+
e
−
i
y
=
ρ
e
−
i
α
Multiplying term to term
1
+
e
i
(
x
−
y
)
+
e
−
i
(
x
−
y
)
+
1
=
ρ
2
or
2
+
2
cos
(
x
−
y
)
=
ρ
2
and finally
cos
(
x
−
y
)
=
a
2
+
b
2
−
2
2
of course
a
,
b
must obey
∣
∣
∣
a
2
+
b
2
−
2
2
∣
∣
∣
≤
1
Answered by
1
Step-by-step explanation:
Sublimation is the transition of a substance directly from the solid to the gas state, without passing through the liquid state.
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