What rules should I look out for when manipulating expressions?

FactoriseFactorise FullyExpandSimplifyExpand and Simplify

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The complicated questions in algebra are really confusing me and I can't seem to be getting the right answers.


Paul travels from Rye to Eston at an average speed of 90 km/h. He travels for T hours. Mary makes the same journey at an average speed of 70 km/h. She travels for 1 hour longer than Paul. Work out the value of T


It is given that sin(x) = 1/2. Find the value of sec(x)


f(x)=cos(x), g(x)=2+cos(x-1), state g(x) as a vector applied to f(x)