# Answer to Question #6652 in Trigonometry for Kyle Trace

Question #6652

(cot^2 betta)/(csc betta)=csc betta-sin betta

Expert's answer

let betta=x for easy writing of

expressions

cot^2(x)/csc(x)=[cos^2(x)/sin^2(x)]/[1/sin(x)]=cos^2(x)/sin(x)=[1-sin^2(x)]/sin(x)=1/sin(x)-sin(x)=csc(x)-sin(x)

expressions

cot^2(x)/csc(x)=[cos^2(x)/sin^2(x)]/[1/sin(x)]=cos^2(x)/sin(x)=[1-sin^2(x)]/sin(x)=1/sin(x)-sin(x)=csc(x)-sin(x)

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