Question

Prove the trig identity sinx(tanx*cosx-cotx*cosx)=1-2cos^2x.

Answer 1

sinx*cosx(tanx-cotx)=1-2cos^2x
sinx*cosx(sinx/cosx-cosx/sinx)=1-2cos^2x
sinx*cosx[sin^2x/(cosx*sinx)-cos^2x/(sinx*cosx)]=1-2cos^2x
sinx*cosx[(sin^2x-cos^2x)/(sinx*cosx)]=1-2cos^2x
sin^2x-cos^2x=1-2cos^2x

Answer 2

Are you done?

Answer 3

No, then I kinda got stuck there.

Answer 4

Did I get something wrong in the process?

Answer 5

replace sin^2x with 1-cos^2x on the left side and you'll be done.

Answer 6

Oh... I can't believe I didn't realize that... looks like I need to go back to familiarizing my fundamental trig identities. Thanks!

Answer 7

yw

Answer 8

*notice