16.) 10cos(β)+9=−2/cos(β)
15.) 2sin(x)−10cos(2x)=−6
14.) Solve for t, 0≤t<2π
15sin2(t)=6tan(t)cos(t)
8.) Solve 6cos(2x)=6cos2(x)−4 for all solutions 0≤x<2π.
10.) Use inverse trig functions to find the smallest two positive solutions of sin(2x+6.5) = 0.8806 on [ 0,2π).
11.) Find all solutions of the equation tan5x−9tanx=0
12.) Find all solutions of the equation sec2x−2=0.
It's not a good idea to submit a long list of problems at once; that gives a bad impression, and often we won't bother answering because it would take too long, or because we just don't want to. Also, be careful pasting; I've had to remove some duplications that are a common result of copying from a source that isn't designed for this. (Compare my quote with your post.)
I'll just make comments on the work you showed for four of the problems. If you need more, you can submit one or two at a time, showing your work and explaining why you are stuck. Please read
this explanation of our guidelines for submission.
On #16, you seem to have done fine, except that there are two angles within [0,2π) whose cosine has any particular value; you gave one in that interval and one that is 2π more. (You haven't indicated whether you were asked for all solutions, or those in some particular interval.)
On #8, you stopped for no good reason. Just subtract one side from the other and continue factoring.
On #10, you seem to be solving a different problem than the #10 you typed. Your work looks good except that you found the wrong two solutions. I would add "+ 2 k π" to each of the two inverse sines, before solving for x, and then find the appropriate values of n.
On #11, just keep going. What are the (real) fourth roots of 9? (Or you could have factored a difference of squares.)