Question

已知tana=1/2，求下列各式的值。 (1)2cosa-3sina/3cosa+4sina (2)sin2a-3sinacosa+4cos2a。谢谢。

Answer 1

(1)原式=(2-3tana)/(3+4tana)=(2-3/2)/(3+2)=1/10
(2)原式=-sinacosa+4(cosa)^2-4(sina)^2=[4(cosa)^2-sinacosa-4(sina)^2]/[(cosa)^2+(sina)^2]
=[4-tana-4(tana)^2]/[1+(tana)^2]
=[4-1/2-1]/[1+1/4]
=2

Answer 2

2cosa-3sina/3cosa+4sina
=(2-3tana)/(3+4tana)
=(2-3/2)/(3+4/2)
=1/2/5
=1/10

sin^2a-3sinacosa+4cos^2a
=(sin^2a-3sinacosa+4cos^2a)/(sin^2a+cos^2a)
=(tan^2a-3tana+4)/(tan^2a+1)
=(1/4-1/2+4)/(1/4+1)
=(15/4)/(5/4)
=3