So the Correct answer would be all three of them.
This includes 27:18, 12:8, and 21:14.
The math behind this includes proportions.
For instance, if you multiple 3 by 9, you get 37. You have to multiple 2 by 9 now, and you should get 18. This is how all three of the answers are correct!
I think we can use the identity sin x/2 = sqrt [(1 - cos x) /2]
cos x - sqrt3 sqrt ( 1 - cos x) /sqrt2 = 1
cos x - sqrt(3/2) sqrt(1 - cos x) = 1
sqrt(3/2)(sqrt(1 - cos x) = cos x - 1 Squaring both sides:-
1.5 ( 1 - cos x) = cos^2 x - 2 cos x + 1
cos^2 x - 0.5 cos x - 0.5 = 0
cos x = 1 , -0.5
giving x = 0 , 2pi, 2pi/3, 4pi/3 ( for 0 =< x <= 2pi)
because of thw square roots some of these solutions may be extraneous so we should plug these into the original equations to see if they fit.
The last 2 results dont fit so the answer is x = 0 , 2pi Answer
Hope I helped, also, I used the math thingy, which I haven't used before, so I'm not sure quite how this turned out, well, I guess we will see in a minute! But if it does not work I can try it just typing regularly.
