How do you simplify #sinx/(1 + sinx) - sinx/(1 -sinx)#?

Question

9792 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-17T01:46:29

You should get #-2tan^2x# as a final answer.

#(sinx)/(1 + sinx) - sinx/(1 - sinx) #

#=(sinx(1 - sinx) - sinx(1 + sinx))/((1 + sinx)(1 - sinx)#

#=(sinx - sin^2x - sinx - sin^2x)/(1 - sin^2x)#

Using the pythagorean identity #cos^2x + sin^2x = 1#

#=(-2sin^2x)/cos^2x#

Using the quotient identity #tanx = sinx/cosx#

#=-2tan^2x#

Hopefully this helps!