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Byju's Answer
Standard XII
Mathematics
Solving Simultaneous Trigonometric Equations
The solution ...
Question
The solution set of the system of equation
x
+
y
=
2
π
3
,
cos
x
+
cos
y
=
3
2
, where
x
and
y
are real, is_______
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Solution
We have
cos
x
+
cos
y
=
3
2
⇒
2
cos
(
x
+
y
2
)
cos
(
x
−
y
2
)
=
3
2
⇒
2
cos
π
3
cos
(
x
−
y
2
)
=
3
2
[using:
x
+
y
=
2
π
/
3
]
⇒
cos
(
x
−
y
2
)
=
3
2
, which is not possible.
Hence, the system of equations has no solution.
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