решите пожалуйста...с подробным объяснением
[tex]2( \cos\frac\pi8 + \sin \frac{\pi}{8})^{2} [/tex]
[tex]2( \cos\frac\pi8 + \sin \frac{\pi}{8})^{2} [/tex]
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Ответ: 2+√2
Пошаговое объяснение:
2×(cosπ/8+sinπ/8)²=2×(cos²π/8+2×cosπ/8×sinπ/8+sin²π/8)
=2×(1+2cosπ/8×sinπ/8)=2×(1+sin2×(π/8)=
2×(1+sinπ/4)=2×(1+√2/2)=2+√2