Question #08381

2 Answers
Mar 21, 2017

Answer:

1

Explanation:

Remember #cot(x) = cos(x)/sin(x)#

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

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

#(cos^4(x)/sin^2(x))/((cos^2(x)-sin^2(x)cos^2(x))/sin^2(x))#

#cos^4(x)/(cos^2(x)-sin^2(x)cos^2(x))#

#cos^4(x)/(cos^2(x)(1-sin^2(x))#

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

Use trig identities, specifically:
#sin^2(x)+cos^2(x)=1#
#cos^2(x)=1-sin^2(x)#

#cos^2(x)/cos^2(x)#

1

Mar 27, 2017

#(cot^2xcos^2x)/(cot^2x-cos^2x)#

#=((csc^2x-1)cos^2x)/(cot^2x-cos^2x)#

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

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

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