Объяснение:

по формулам привидения:

1).

[tex]cos {135}^{0} = cos( {90}^{0} + {45}^{0} ) = - sin {45}^{0} = - \frac{ \sqrt{2} }{2} [/tex]

2).

[tex]sin \frac{8\pi}{3} = sin( \frac{9\pi}{3} - \frac{1\pi}{3} ) = sin(3\pi - \frac{\pi}{3} ) = sin \frac{\pi}{3} = \frac{ \sqrt{3} }{2} [/tex]

3).

[tex]tg \frac{7\pi}{3} = tg( \frac{6\pi}{3} + \frac{\pi}{3}) = tg(2\pi + \frac{\pi}{3} ) = tg \frac{\pi}{3} = \sqrt{3} [/tex]

4).

формула косинус двойного аргумента:

[tex]cos2 \alpha = {cos}^{2} \alpha - {sin}^{2} \alpha [/tex]

[tex] {cos}^{2} \frac{\pi}{8} - {sin}^{2} \frac{\pi}{8} = \\ = cos(2 \times \frac{\pi}{8} ) = \\ = cos \frac{\pi}{4} = \frac{ \sqrt{2} }{2} [/tex]