Expert: Paul Klarreich - 7/16/2009

Question
prove the following:square secantx + square cosecantx =
square secant *square cosecantx

Answer
Questioner:   aiza
Country:  Philippines
Category:  Advanced Math
Private:  No
 
Subject:  trigonometric identities
Question:  prove the following:square secantx + square cosecantx =
square secant *square cosecantx
.....................................
Hi, Aiza,
 
sec^2(x) + csc^2(x) = sec^2(x) csc^2(x)
  1          1
------- + --------  << reciprocal identities
cos^2(x)  sin^2(x)

sin^2(x) + cos^2(x)
--------------------  << combine fractions
cos^2(x)  sin^2(x)

        1
--------------------  << Pythagorean identity
cos^2(x)  sin^2(x)

  1           1
---------  -----------  << Split into two fractions
cos^2(x)    sin^2(x)

sec^2(x) csc^2(x)    << Guess what!