Тригонометрия cosx=1/2. (12sin^2x+3sin3x+2cos2x+2)

[scarlet]

cosx=1/2. (12sin²x+3sin3x+2cos2x+2)

*това в скобите, цялото е под корен

[Xixibg]

[tex]cosx=\frac{1}{2} ; =>sin^2x=\frac{3}{4} ; cos^2x=\frac{1}{4}[/tex]
[tex]cos2x=cos^2x-sin^2x=-\frac{1}{2}[/tex]
[tex]sin3x=sin(x+2x)=sinx.cos2x+sin2x.cosx=sinx(cos2x+2cos^2x)=0[/tex]
[tex]=>\sqrt{12sin^2x+3sin3x+2cos^2x+2}=\sqrt{9+0+\frac{1}{2}+2}=\frac{\sqrt{46}}{2}[/tex]