limx-->0
cosx^(cosecx)=
e^(ln(cosx^(cosecx))=
e^( cosecx lncosx)=
e^ ( limx-->0 ( (lncosx)/sinx)....(1)
limx-->0 ( (lncosx)/sinx).=
limx-->0 ( -(1/cosx)sinx )/cosx
limx-->0 ( -sinx/cos²x).=0
e^ ( limx-->0 ( (lncosx)/sinx)=e^0=1
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limx-->0
cosx^(cosecx)=
limx-->0
e^(ln(cosx^(cosecx))=
limx-->0
e^( cosecx lncosx)=
e^ ( limx-->0 ( (lncosx)/sinx)....(1)
limx-->0 ( (lncosx)/sinx).=
limx-->0 ( -(1/cosx)sinx )/cosx
limx-->0 ( -sinx/cos²x).=0
e^ ( limx-->0 ( (lncosx)/sinx)=e^0=1