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Problem
Problem
Find the solutions of the equation
(
sin
x
+
cos
x
)
sin
2
x
=
a
(
sin
3
x
+
cos
3
x
)
(\sin x + \cos x) \sin 2x = a(\sin^3 x + \cos^3 x)
(
sin
x
+
cos
x
)
sin
2
x
=
a
(
sin
3
x
+
cos
3
x
)
located between
π
2
\frac{\pi}{2}
2
π
and
π
\pi
π
and for which values of 'a' does this equation have at most one solution satisfying the condition
π
2
≤
x
≤
π
\frac{\pi}{2} \le x \le \pi
2
π
≤
x
≤
π
.
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