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Surprising FullSimplify result


Here's what I am getting

Cos[theta]^2 + Sin[theta]^2 // FullSimplify
Out[540]= 1

Cos[theta]^2 + Sin[theta]^2 + L^2 Cos[theta]^2 // FullSimplify
Out[541]= 1/2 (2 + L^2 + L^2 Cos[2 theta])

I'm really surprised that the answer in the latter case is not

1+ L^2 Cos[theta]^2

Is there an explanation?

Thanks,

Sam


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