Question

use the fundamental identities to simplify the expression

cos (raised to the 2nd power) X
----------------------------------------- + csc X sin X
sin (raised to the 2nd power) X

Answer 1

we know that csc(X)=1/sin(X). So
cos^2(X)/sin^2(X)+csc(X)*sin(X)=cos^2(X)/sin^2(X)+1/sin(X)*sin(X)=
=cos^2(X)/sin^2(X)+1=(cos^2(X)+sin^2(X))/sin^2(X)=1/sin^2(X)