The equation given is right next to each number...all work under that is mine...I believe the first four should be correct, but I am having trouble from number 5-8...could someone please assist me?
5 & 6 are easily shown with the Pythagorean Identity.
In 5, there is a preponderance of sin(x), so solve for $\displaystyle \cos^{2}(x)\;=\;1\;-\;\sin^{2}(x)$ and substitute. You will be left with a bunch of sines that you can handle.
In 6, there is a preponderance of cos(x), so solve for $\displaystyle \sin^{2}(x)\;=\;1\;-\;\cos^{2}(x)$ and substitute. You will be left with a bunch of cosines that you can handle.