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Answer to Question #19795 in Trigonometry for kevin

Question #19795
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
Expert's answer
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)

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