6cos^2 x+5cos (pi/2-x) = 7

6cos^2x+5cos (π/2-x) - 7=0

6cos^2+5sinx-7=0

6 (1-sin^2x) + 5sinx-7=0

6-6sin^2x+5sinx-7=0

-6sin^2x+5sinx-1=0

6sin^2x-5sinx+1=0

sinx=t t по модулю≤1

6t^2-5t+1=0

D=25-4*6*1=1

t1 = 5+1/12=1/2

t2=5-1/12=1/3

sinx=1/2 sinx=1/3

x=π/6+2πn; n∈z x=arcsin1/3+2πn; n∈z

x=5π/6+2πn; n∈z x=π-arcsin1/3+2πn; n∈z