What is the difference between the equity method and cost method in consolidated statement?

Are you talking about Leases. Leases can be reported on the Balance Sheet (Equity method) or the Incomes statement (Cost method). The Equity method is for leases where you will own the eequipment and Cost method is where you do not or will not have ownership rights (like renting a copier for 3 months then returning it to the lessor).