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t->0
(sint)^2 = t^2 +o(t^2)
cost = 1-(1/2)t^2 +o(t^2)
(sint)^2+ cost = 1+(1/2)t^2 +o(t^2)
ln[(sint)^2+ cost]
=ln[ 1+(1/2)t^2 +o(t^2)]
=(1/2)t^2 +o(t^2)
lim(t->0) ln[ (sint)^2+ cost ]/t^2
=lim(t->0) (1/2)t^2/t^2
=1/2
(sint)^2 = t^2 +o(t^2)
cost = 1-(1/2)t^2 +o(t^2)
(sint)^2+ cost = 1+(1/2)t^2 +o(t^2)
ln[(sint)^2+ cost]
=ln[ 1+(1/2)t^2 +o(t^2)]
=(1/2)t^2 +o(t^2)
lim(t->0) ln[ (sint)^2+ cost ]/t^2
=lim(t->0) (1/2)t^2/t^2
=1/2
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