证：
sin2θ=5cos^2θtana
2sinθcosθ=5cos^2θtana
2sinθ=5cosθtana
tanθ=5/2tana
左=tan(θ+a)
=(tanθ+tana)/(1-tanθtana)
=(5/2tana+tana)/(1-5/2tana*tana)
=(5tana+2tana)/(2-5tan^2a)
=7tana/(2-5tan^2a)
=7/(2/tana-5tana)
=7/(2cosa/sina-5sina/cosa)
=7/(2cos^2a-5sin^2a)/sinacosa
=7/2sin2a/[2cos^2a-5(1-cos^2a]
=7/2sin2a/(7cos^2a-5)
=7/2sin2a/(14cos^2a-10)/2
=7/2sin2a/[(14cos^2a-7)-3]/2
=7sin2a/(7cos2a-3)=右
证毕