Question

若tanθ=2.则(sin2θ-cos2θ)/1+cos^2θ等于

Answer 1

(sin2θ-cos2θ)/(1+cos^2θ)

=[2sinθcosθ-(cosθ)^2+(sinθ)^2]/[(sinθ)^2+(cosθ)^2+(cosθ)^2]

【分子分母都除以(cosθ)^2】

=[2tanθ+(tanθ)^2-1]/[(tanθ)^2+2]

=(2×2+2^2-1)/(2^2+2)

=7/6