Question

Сделайте, пожалуйста. 35 баллов​

Answer 1

Ответ:

2

Объяснение:

cos(3a/2)*cos(a/2)=1/2

cos(3a/2)*cos(a/2) =

= (1/2) * ( cos(3a/2 + a/2) + cos (3a/2 - a/2) ) =

= (1/2) * (cos (4a/2) + cos (2a/2) ) =

= (1/2) * (cos (2a) + cos(a)) =

= (1/2) * (2 cos² a - 1 + cos a) = 1/2

(2 cos² a - 1 + cos a) = (1/2) : (1/2)

(2 cos² a - 1 + cos a) = 1 →

→ 2 * (2 cos² a + cos a - 1) = 2*1 = 2

Answer 2

Ответ:

$cos\dfrac{3a}{2}\cdot cos\dfrac{a}{2}=\dfrac{1}{2}\cdot \Big(cos(\frac{3a}{2}+\frac{a}{2})+cos(\frac{3a}{2}-\frac{a}{2})\Big)=\dfrac{1}{2}\cdot \Big(cos2a+cosa\Big)=\dfrac{1}{2}\ \ \Rightarrow \\\\\\cos2a+cosa=1\\\\(cos^2a-sin^2a)+cosa=1\\\\\Big(cos^2a-(1-cos^2a)\Big)+cosa=1\\\\\Big(2cos^2a-1\Big)+cosa=1\\\\\underline{\ 2cos^2a+cosa-1=1\ }\\\\\\2\, \Big(\underbrace{2cos^2a+cosa-1}_{1}\Big)=2\cdot 1=2$