Question

Упростите выражение: 1/8 * cos4a + 0,5cos2a + 3/8 = ?

Answer 1

$\dfrac{1}{8}\cos4\alpha+0{,}5\cos2\alpha+\dfrac{3}{8}=\dfrac{1}{8}\Big(\cos 4\alpha+3\Big)+0{,}5\cos 2\alpha=\dfrac{1}{8}\Big(2\cos^22\alpha-1+\\ \\ +3\Big)+0{,}5\cos2\alpha=\dfrac{1}{4}\Big(\cos^22\alpha+1\Big)+0{,}5\cos2\alpha=\\ \\ =\left(\dfrac{\cos2\alpha}{2}\right)^2+\dfrac{\cos2\alpha}{2}+\left(\dfrac{1}{2}\right)^2=\left(\dfrac{\cos2\alpha+1}{2}\right)^2=\Big(\cos^2\alpha\Big)^2=\cos^4\alpha$

Answer 2

Ответ:сos⁴α

Объяснение:(1/8)*(2cos²2α-1)+(1/2)cos2α+3/8=(1/4)(cos²2α+1+2cos2α)

=(1/4)(cos2α+1)²=(2cos²α-1+1)²/4=cos⁴α