Question

已知sin(3π+a)=2sin(3π/2+a),求下列各式的值sina-4cosa/5sina+2cos2a

Answer 1

sin(3π+a)=2sin(3π/2+a),
左边
=sin(3π/2+3π/2+a)
=sin(3π/2)cos(3π/2+a)+sin(3π/2+a)cos(3π/2)
=-cos(3π/2+a)
=cos(π/2+a)
=-sina
右边
=2sin(3π/2+a)
=-2sin(π/2+a)
=-2cosa
所以
-sina=-2cosa
tana=2

分母上是不是 5sina+2cosa ?

(sina-4cosa)/(5sina+2cosa)
分子分母同时处以cosa得
=(tana-4)/(5tana+2)
=(2-4)/(10+2)
=-1/6