Prove that $(tanx-cotx)/(tanx+cotx)=1-2cos^2x$ ?

Question

5804 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-04T01:51:50

that $(tanx-cotx)/(tanx+cotx)=-cos2x$

but $cos2x=cos^2x-sin^2x=cos^2x-(1-cos^2x)=2cos^2x-1$

substitute the last to the result we found to get what you want.

Prove that (tanx-cotx)/(tanx+cotx)=1-2cos^2x(tanx-cotx)/(tanx+cotx)=1-2cos^2x?