do you ever drop your broadest keywords in secondary pages?

[GirlPower19]

I know that on my index page i am supposed to have the most broad keywords... and than on my secondary pages it is supposed to be more specific... and on my third and forth pages my keywords should be the most niched....
Now my question is this.... Should i still be including my broadest keywords in all of my pages. For example... if i sell cars... the keyword CAR will be in my first pages keywords... however in my second page i may get into car parts, car prices, car shops, car models... and than my third page... motors, engines, rims, etc. Would i still include the word CAR in my keywords on these secondary pages... or does that defeet the purpose of becoming more niched?

Thanks for you help guys!
GIRRRRRRRRLPOWER hahah LOL

[incrediBILL]

I always spell it out 100% with BROAD KEY > NARROW KEY > NARROWER KEY, etc. and and I've done this on many sites and it helped a bunch, be as completely specific as possible. Each page / topic needs to clearly 100% identify exactly what it is and it will probably rank well in the right spot.

In your case I could explicitly specify "CAR MOTORS", "CAR ENGINES", etc. as there are many other types of motors, and engines, get the idea? Specific as possible, no ambiguity, the only way to fly.