Solving trigonometric equations involving multiple angles

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Lessons
  1. Solve the following equations
    i) State the general solution
    ii) 0x2π0 \leq x \leq 2\pi
    1. sin3x=12\sin 3x = - {1 \over 2}
    2. cos2x=22\cos 2x = {\sqrt2 \over 2}
    3. tanx2=1\tan {x \over 2} = -1
    4. 3sin22x7sin2x=15sin2x3\sin^2 2x -7 \sin 2x = 1 - 5 \sin 2x
  2. Solve: sin2xcos2x=0\sin 2x - \cos 2x = 0
    180x180 -180^\circ \leq x \leq 180^\circ