You can find the magnitude of cos(a). You also know that a is in QIV, so what does that mean for the sign of cos(a)?
b) You now know sin(a) and cos(a), how do you find tan(a)?
Do d) next.
You can find sec(b) from this. (Remember that b is in QIII.) How does sec(b) relate to cos(b)?
c) You can use the sin squared equation here, or recall how tan(b) is defined in terms of sin(b) and cos(b) (and then use d).)
For the rest see here. You are looking specifically for the "Angle Sum and Difference Identities" and the "Double, Triple, and Half-Angle Formulae" sections.