a) A is a hard one but here goes...
[tex]4cos2x + 2sinx = 3\\4cos2x + 2sinx -3 = 0\\4(1-sin^2x) +2 sinx - 3 = 0\\let w = sinx\\4(1-2w^2) + 2w -3 = 0\\8w^2 + 2w - 3 = 0\\factor\\\\(2w-1)(4w+3)=0\\\\w = sinx = \frac{1}{2},\frac{-3}{4\\}\\x= arcsin(\frac{1}{2}) = \frac{\pi}{6} + 2k\pi \\\\and \\x =arcsin(\frac{-3}{4} )+2k\pi[/tex]
b)
[tex]sin2x = sin2x\\sin2x - sin2x = 0[/tex]
x = all real numbers
c)
[tex]7sinx*cosx =2\\7 * \frac{sin2x}{2} = 2\\7*sin2x = 4\\sin2x = \frac{4}{7}\\2x = arcsin(4/7)\\x = \frac{arcsin\frac{4}{7} }{2}+2\pi k[/tex] where k is an integer.
