Question

Вычислите: sin(pi/8)*cos(pi/8)+1/4

Answer 1

$\sin \dfrac{\pi }8\cdot \cos \dfrac{\pi}8 + \dfrac 14=\dfrac 12\cdot\Big(2\sin \dfrac{\pi }8\cdot \cos \dfrac{\pi}8\Big) + \dfrac 14=\\\\\\=\dfrac 12\cdot \sin \dfrac {\pi}4+\dfrac 14=\dfrac 12\cdot \dfrac {\sqrt 2}2+\dfrac 14=\dfrac {\sqrt 2+1}4$

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Использована формула

2 · sin α · cos α = sin (2α)