求证;3-2cos^2α=3tan^2+1/tan^2α+1

求证;3-2cos^2α=3tan^2+1/tan^2α+1
求证;3-2cos^2α=3tan^2+1/tan^2α+1

求证;3-2cos^2α=3tan^2+1/tan^2α+1
左=3-2cos²α=3(cos²α+sin²α)-2cos²α=3sin²α+cos²α
右=(3tan²α+1)/(tan²α+1)
=(3sin²α/cos²α+1)/(sin²α/cos²α)
=(3sin²α+cos²α)/(sin²α+cos²α)
=3sin²α+cos²α
∴ 左=右
∴ 3-2cos^2α=3tan^2+1/tan^2α+1