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

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)

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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