Question

已知函数f(x)=sin^2(x)+2根号3sinxcosx+5cos^2(x) (1)若f(a)=5,求tana的值；

Answer 1

∵f(a)=5

∴sin²a + 2√3sinacosa + 5cos²a=5

sin²a + 2√3sinacosa=5 - 5cos²a

sin²a + 2√3sinacosa=5(1 - cos²a)

sin²a + 2√3sinacosa=5sin²a

2√3sinacosa=4sin²a

1=(4sin²a) / (2√3sinacosa)

1=(2/√3)tana

tana=√3/2

2.3-4cos2a+cos4a / 3+4cos2a+cos4a

=3-4cos2a+(2cos²2a-1) / 3+4cos2a+(2cos²2a-1)

=2cos²2a-4cos2a+2 / 2cos²2a+4cos2a+2

=2(cos2a-1)² / 2(cos2a+1)²

={[(1-tan²a)/(1+tan²a)]-1}² / {[(1-tan²a)/(1+tan²a)]+1}²

=9/16