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Simplify with assumptions


Using Mathematic 4.1, Why won't the 2nd expression simplify?

Simplify[1 - c^2,  s^2 + c^2 == 1]
gives
s^2

But
Simplify[1 - s^2,  s^2 + c^2 == 1]
gives
1 - s^2

Why doesn't this 2nd expression yield c^2?

The leaf count of both s^2 and c^2 are 3.
While the leaf count for both 1 - s^2 and 1 - c^2 are 7.













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