Explanation:
3. Let us take apart the right side
1+cos2x = 1 + cos^2x - sin^2x
1 - sin^2x = cos^2x
therefore we have 2cos^2x
Therefore we just have cos^2x/cos^2y = 2cos^2x/2cos^2y, which is true.
4. tan(x/2) = +/- sqrt((1-cosx)/(1+cosx)) using half angle identities for sin and cos.
Therefore tan^2(x/2) = (1-cosx)/(1+cosx)
If we multiply top and bottom by tanx, we get
(tanx - sinx)/(tanx + sinx), which is the right side.