Question #5a859

1 Answer
sente
Aug 14, 2016

We will start from the left hand side and show that it equals the right hand side. To do so, we will use the following identities:

  • #tan(x) = sin(x)/cos(x)#
  • #sec(x) = 1/cos(x)#
  • #sec^2(x) - 1 = tan^2(x)#

Note that the third identity may be derived from #sin^2(x) + cos^2(x) = 1# by dividing each side by #cos^2(x)# and then subtracting #1# from each side.

Proceeding:

#LHS = tan^2(u) - sin^2(u)#

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

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

#=sin^2(u)(1/cos^2(u) - 1)#

#=sin^2(u)(sec^2(u)-1)#

#=sin^2(u)tan^2(u) = RHS# ∎

Related questions
See all questions in Proving Identities
Impact of this question
900 views around the world
You can reuse this answer
Creative Commons License