Official solution
sin7x \[\le\] sin2x \[\le\] 1 ...... (1)
and cos7x \[\le\] cos2x \[\le\] 1 ..... (2)
also sin2x + cos2x = 1
\[\Rightarrow\] equality must hold for (1) \& (2)
\[\Rightarrow\] sin7x = sin2x \& cos7x = cos2x
\[\Rightarrow\] sin x = 0 \& cos x = 1
or
cos x = 0 \& sin x = 1
\[\Rightarrow\] x = 0, 2\[\pi\], 4\[\pi\], \[{\pi \over 2},{{5\pi } \over 2}\]
\[\Rightarrow\] 5 solutions