I am very confused too, but I'll try my best.

**question 1**

cos(x) = sqrt(1-sine(x)^2)

cos(x) = sqrt(1 - (-6k/(k^2+9))^2)

cos(x) = sqrt(1-(36k^2)/(k^4+18k^2+81))

cos(x) = sqrt((k^4-18k^2+81)/(k^4+18^2+81))

cos(x) = (k^2-9)/(k^2+9)

**question 2**

tan(x)+1/cos(x) = tan(x)+1/cos(x)

tan(x)+1/cos(x) = sine(x)/cos(x) + 1/(cos(x))

tan(x)+1/cos(x) = (sine(x)+1)/cos(x)

tan(x)+1/cos(x) = (-6k/(k^2+9)+1)/((k^2-9)/(k^2+9))

tan(x)+1/cos(x) = ((k^2-6k+9)/(k^2+9))/((k^2-9)/(k^2+9))

tan(x)+1/cos(x) = ((k^2-6k+9)*(k^2+9))/((k^2+9)*(k^2-9))

tan(x)+1/cos(x) = (k^2-6k+9)/(k^2-9)

tan(x)+1/cos(x) = (k-3)(k-3)/(k+3)(k-3)

tan(x)+1/cos(x) = (k-3)/(k+3)

I am about 99% that I am wrong, but I hope this helped. :))

=^._.^=