证明tanα-cotα=(1-2cos^2α)/(sinαcosα)

问题描述:

证明tanα-cotα=(1-2cos^2α)/(sinαcosα)

tanα-cotα=sinα/cosα-cosα/sinα=(sin²α-cos²α)/sinαcosα=(1-cos²α-cos²α)/sinαcos=(1-2cos²α)/sinαcosα

tanα-cotα
=sinα/cosα-cosα/sinα
=[sin^2α-cos^2α)/sinαcosα
=(1-2cos^2α)/sinαcosα