数学三角函数若f(x)=2sin(x+α)+3cos(x-α)是偶函数,则tanα=?
2019-05-27
数学三角函数
若f(x)=2sin(x+α)+3cos(x-α)是偶函数,则tanα=?
优质解答
f(-x)=2sin(-x+α)+3cos(-x-α)=f(x)=2sin(x+α)+3cos(x-α)
-2sin(x-α)+3cos(x+α)=f(x)=2sin(x+α)+3cos(x-α)
-2sinxcosα+2cosxsinα+3cosxcosα-3sinxsinα
=2sinxcosα+2cosxsinα+3cosxcosα+3sinxsinα
4sinxcosα-6sinxsinα=0
4cosα=6sinα
tanα=3/2
f(-x)=2sin(-x+α)+3cos(-x-α)=f(x)=2sin(x+α)+3cos(x-α)
-2sin(x-α)+3cos(x+α)=f(x)=2sin(x+α)+3cos(x-α)
-2sinxcosα+2cosxsinα+3cosxcosα-3sinxsinα
=2sinxcosα+2cosxsinα+3cosxcosα+3sinxsinα
4sinxcosα-6sinxsinα=0
4cosα=6sinα
tanα=3/2