已知f(x)=(2sinθcosθ+5/2)/sinθ+cosθ1求f(π/12)2求f(x+1)的解析式

Question

已知f(x)=(2sinθcosθ+5/2)/sinθ+cosθ
1 求f(π/12)
2 求f(x+1)的解析式

Answer 1

f(x)=(2sinxcosx+5/2)/sinx+cosx
=3cosx+5/(2sinx)
π/12=15(省略度)
cos(15)=cos(45-30)=cos45cos30+sin45sin30=√6/4+√2/4
sin(15)=(√6-√2)/4
1/sin(15)=√6+√2
f(π/12)=3(√6+√2)/4+10(√6+√2)/4=13(√6+√2)/4
f(x+1)=3cos(x+1)+5/[2sin(x+1)]