sin 7 x $\le$ sin 2 x $\le$ 1 ...... (1) and cos 7 x $\le$ cos 2 x $\le$ 1 ..... (2) also sin 2 x + cos 2 x = 1 $\Rightarrow$ equality must hold for (1) & (2) $\Rightarrow$ sin 7 x = sin 2 x & cos 7 x = cos 2 x $\Rightarrow$ 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