已知tanα=3,求4sin²α+3sinα×cos+6cos²α的值.

已知tanα=3,求4sin²α+3sinα×cos+6cos²α的值.

4sin²α+3sinα×cosα+6cos²α
=(4sin²α+3sinα×cosα+6cos²α)/(sin²α+cos²α)
分子分母同除以cos²α
=(4tan²α+3tanα+6)/(tan²α+1)
=(4*9+3*3+6)/(9+1)
=51/10