5.设a为第四象限的角,若sin3a/sina=13/5,则tan2a=?6.已知sin(π/4+2a).sin(π/4-2a)=1/4,a∈（π/4,π/2）,求2sin��a+tana-1/tana-1的值.7.已知-π/2

Question

5.设a为第四象限的角,若sin3a/sina=13/5,则tan2a=?
6.已知sin(π/4+2a).sin(π/4-2a)=1/4,a∈（π/4,π/2）,求2sin��a+tana-1/tana-1的值.
7.已知-π/2

Answer 1

5题答案
sin3a
=sin2a*cosa+cos2a*sina
=2sina*cosa^2+(cosa^2-sina^2)*sina
=3sina*cosa^2-sina^3
=sina(3cos^2-sina^2)
sin3a/sina
=3cos^2-sina^2
=3cos^2-(1-cos^2)
=4cos^2-1
=5/13
解的cosa^2=9/10由于a为第四象限的角故cosa=3√10,sina=-1√10
sin2a=2sina*cosa
=-3/5