Question

若tanα=3，则2sin 2 α+3sinα?cosα+5cos 2 α的值是______

若tanα=3，则2sin 2 α+3sinα?cosα+5cos 2 α的值是______．

Answer 1

∵tanα=3， ∴2sin 2 α+3sinα?cosα+5cos 2 α = 2 sin 2 α+3sinα?cosα+5 cos 2 α  sin 2 α+ cos 2 α = 2 tan 2 α+3tanα+5 tan 2 α+1 = 2× 3 2 +3×3+5 3 2 +1 = 16 5 ． 故答案为： 16 5