Question

6cos²x+5cos(p/2+x)=7

Answer 1

$6cos^2x+5cos( dfrac{ pi }{2}+x)=7 \ 6(1-sin^2x)-5sinx-7=0 \ 6sin^2x+5sinx+1=0 \ \ sinx=a \ \ 6a^2+5a+1=0 \ D=25-24=1 \ a_1= dfrac{-5-1}{12}=-0,5 \ a_2= dfrac{-5+1}{12}=- dfrac{1}{3} \ \ 1) \ sinx=-0,5 \ \ x= dfrac{7 pi }{6}+2 pi k; k in Z \ \ \ x= pi - dfrac{7 pi }{6}+2 pi k; k in Z \ x=- dfrac{ pi }{6}+2 pi k; k in Z \ \ 2) \ sinx=- dfrac{1}{3} \ \ x=arcsin(- dfrac{1}{3})+2 pi k; k in Z \ \ x= pi -arcsin(- dfrac{1}{3})+2 pi k; k in Z$