Show that '2sinx = (4cosx -1) / (tanx)' can be written as '6cos^2(x) - cosx - 2 = 0'

This is likely to be a 3 mark question in an exam.Original equation: 2sinx = (4cosx - 1) / tanxNote that the final equation is written in terms of cosx only. Therefore, we should try to use identities to convert the sinx and tanx in to cosx[1] Identity: tanx = sinx / cosxso sinx = (tanx)(cosx)[2] Substitute [1] into the original equation:2(tanx)(cosx) = (4cosx - 1) / tanx[3] tanx still remains. Let's group the tanx terms together:2(tan²x)(cosx) = 4 cosx - 1[4] Identity: 1 + tan²x = sec²xso tan²x = sec²x - 1[5] Substitute [4] into [3]:(2cosx)(sec²x - 1) = 4cosx - 1[6] Expand the brackets and rearrange, remembering that secx = 1 / cosx:(2cosx / cos²x) - 2cosx = 4cosx - 12 / cosx = 6cosx - 12 = 6cos²x - cosx6cos²x - cosx - 2 = 0 as required