How do you perform multiplication and use the fundamental identities to simplify #(cotx+cscx)(cotx-cscx)#?

2 Answers
Aug 22, 2017

#-1#

Explanation:

we start with the difference of squares expression

#(a+b)(a-b)=a^2-b^2#

Applying that here we have

#(cotx+cscx)(cotx-cscx)=cot^2x-csc^2x#

now the identity connecting # cotx" & "cscx" is as follows"#

#cot^2x+1=csc^2x#

substituting for # csc^2x#

#=cot^2x-(cot^2x+1)#

#=cancel(cot^2x-cot^2x)-1#

#=-1#

Aug 22, 2017

#-1#

Explanation:

#"using the "color(blue)"trigonometric identities"#

#•color(white)(x)cotx=cosx/sinx" and "cscx=1/sinx#

#•color(white)(x)cos^2x=1-sin^2x#

#"expand the factors using the FOIL method"#

#rArr(cotx+cscx)(cotx-cscx)#

#=cot^2x-csc^2x#

#=cos^2x/sin^2x-1/sin^2xlarr" common denominator"#

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

#=(cancel(1)-sin^2xcancel(-1))/sin^2x#

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

#=-1#