# Answer to Question #25415 in Abstract Algebra for Melissa

Question #25415

tan^2(x)csc^2(x)-tan^2(x)

Expert's answer

tan^2(x)csc^2(x)-tan^2(x)=tan^2(x) *(csc^2(x)-1)=tan^2(x)*( 1/sin^2(x) -1)=tan^2(x)*( (1-sin^2(x) )/sin^2(x)

)=tan^2(x) * cos^2(x)/sin^2(x)=( sin^2(x)/cos^2(x) ) * cos^2(x)/sin^2(x)=1

)=tan^2(x) * cos^2(x)/sin^2(x)=( sin^2(x)/cos^2(x) ) * cos^2(x)/sin^2(x)=1

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