Show that 2(1-cos(x)) = 3sin^2(x) can be written as 3cos^2(x)-2cos(x)-1=0.

Firstly let's expand out the staring equation getting rid of any brackets. This gives: 2-2cos(x)) = 3sin^2(x). Now we can spot that the sin^2(x) term is in the first equation but no the final one. So let's try and remember a trig identity which could be used to convert sin^2(x) into cos^2(x). The trig identity needed is: cos^2(x) + sin^2(x) = 1. Rearrange to make sin^2(x) the subject (1-cos^2(x) =sin^2(x)) and substitute: 2-2cos(x)) = 3(1-cos^2(x)). Again expand out the brackets: 2-2cos(x)) = 3-3cos^2(x). Then we can minus 3 from the LHS and add 3cos^2(x) to the LHS to collect all the terms on one side of the equation giving us: 3cos^2(x)-2cos(x)-1=0. That's the final equation asked for in the question so we're done!