For number one, use the identity: a^3-b^3=(a-b)(a^2+ab+b^2)

Number 2

Place the L.H.S. under a common denominator and solve from there

Number 3

Use (1-sin^2r)=cos^2r on the R.H.S.

Number 4

Do the same thing as number 2

Number 5

A bit more tricky

becomes

becomes

Solve from there