Так он уже за скобками...не понятно...может просто нужно решить эти примеры
Sin a + cos a = 1/2,
(sin a + cos a)^2 = 1/2,
sin^2 a + 2*(sin a)*(cos a) + cos^2 a = 1/2,
1 + 2*(sin a)*(cos a) = 1/2
2*(sin a)*(cos a) = -1/2
<span>(sin a)*(cos a) = -1/4. </span>
![P_n = n!](https://tex.z-dn.net/?f=P_n+%3D+n%21)
1)
![\frac{P_6 - P_5}{5!} = \frac{6! - 5!}{5!} = 6 - 1 = 5](https://tex.z-dn.net/?f=%5Cfrac%7BP_6+-+P_5%7D%7B5%21%7D+%3D+%5Cfrac%7B6%21+-+5%21%7D%7B5%21%7D+%3D+6+-+1+%3D+5)
2)
![\frac{P_n}{n(n-1)} = \frac{n!}{n(n-1)} = \frac{1*2*3*\cdots*n}{n(n - 1)} = (n - 2)! = P_{n - 2}](https://tex.z-dn.net/?f=%5Cfrac%7BP_n%7D%7Bn%28n-1%29%7D+%3D+%5Cfrac%7Bn%21%7D%7Bn%28n-1%29%7D+%3D+%5Cfrac%7B1%2A2%2A3%2A%5Ccdots%2An%7D%7Bn%28n+-+1%29%7D+%3D+%28n+-+2%29%21+%3D+P_%7Bn+-+2%7D)
3)
![C^2_{x} = 153 \\\\C^2_{x} = \frac{x!}{2(x - 2)!} = \frac{x(x - 1)}{2} = 153 \\\\x^2 - x - 306 = 0 \\\\x_1 = 18 \\x_2 = -17 (!) \\\\x = x_1 = 18](https://tex.z-dn.net/?f=C%5E2_%7Bx%7D+%3D+153+%5C%5C%5C%5CC%5E2_%7Bx%7D+%3D+%5Cfrac%7Bx%21%7D%7B2%28x+-+2%29%21%7D+%3D+%5Cfrac%7Bx%28x+-+1%29%7D%7B2%7D+%3D+153+%5C%5C%5C%5Cx%5E2+-+x+-+306+%3D+0+%5C%5C%5C%5Cx_1+%3D+18+%5C%5Cx_2+%3D+-17+%28%21%29+%5C%5C%5C%5Cx+%3D+x_1+%3D+18)
Тут не уверен, что верно понял.
4) Скорее всего, количество перестановок ![P_4 = 4! = 24](https://tex.z-dn.net/?f=P_4+%3D+4%21+%3D+24)
5) А тут, скорее всего, количество сочетаний ![C^3_7 = \frac{7!}{3!4!} = 35](https://tex.z-dn.net/?f=C%5E3_7+%3D+%5Cfrac%7B7%21%7D%7B3%214%21%7D+%3D+35)
<span>(5c-1)(5c+1)=(5c)</span>²-1²=25c²-1.