Question

已知tan a=2 ,2sin a cos a=?(sina)^2-sin a cos a -2(cos a)^2=?

Answer 1

利用sin^2 a+cos^2 a=1,

2sin a cos a

=2sin a cos a/(sin^2 a+cos^2 a)

=2tana/(tan^2 a+1)

=2x2/(4+1)

=4/5.

(sina)^2-sin a cos a -2(cos a)^2

=[(sina)^2-sin a cos a -2(cos a)^2]/(sin^2 a+cos^2 a)

=(tan^2 a-tan a -2)/(tan^2 a+1)

=(4-2-2)/(4+1)

=0.