How to prove this identity? #sin^2x+tan^2x * sin^2x= tan^2x#

2 Answers
Mar 18, 2018

Shown below...

Explanation:

Use our trig identities...

#sin^2 x + cos^2 x =1 #

#=> sin^2 x / cos^2 x + cos^2 x / cos^2 x = 1 / cos^2 x #

#=> tan^2 x + 1 = 1/cos^2 x #

Factor the left side of your problem...

#=> sin^2 x ( 1 + tan^2 x ) #

#=> sin^2 x ( 1/cos^2 x ) = sin^2 x / cos^2 x #

#=> (sinx/cosx)^2 = tan^2 x #

Mar 18, 2018

Given,

#sin^2 x +tan^2x sin^2x#

#=sin^2 x(1+tan^2 x)#

#=sin ^2 x sec ^2x# (as,# sec^2x - tan^2 x=1)#

#= sin ^2x (1/(cos ^2x))#

#=tan^2 x#

              Proved