prove the identity cotx-cot2x=cosec2x

cotx-cot2x=cosec2x
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cot(x)-cot(2x)=1/tan(x)-1/tan(2x)=1/tan(x)-(1-tan2(x))/(2tan(x)),

cot(x)-cot(2x)=(1/tan(x))(1-½(1-tan2(x))=(1/tan(x)(1+tan2(x))/2,

cot(x)-cot(2x)=½(cos(x)/sin(x))sec2(x)=1/(2sin(x)cos(x))=1/sin(2x)=cosec(2x) QED

by Top Rated User (1.2m points)

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