已知tana=-1/3,计算1/(2sinacosa+cos2a)

问题描述:

已知tana=-1/3,计算1/(2sinacosa+cos2a)

1/(2sinacosa+cosa^2a)
=(sin^2a+cos^2a)/(2sinacosa+cosa^2a)
=[(sin^2a+cos^2a)/cos^2a]/[(2sinacosa+cosa^2a)/cos^2a]
=(tan^2a+1)/(2tana+1)
=[(-1/3)^2+1]/[2*(-1/3)+1]
=10/3