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Question

Prove that cotx.cot2xcot2x.cot3xcotx.cot3x=1

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Solution

cot x cot 2x - cot 2x cot 3x - cot 3x cot 4x
= cot x cot 2x - cot 3x (cot 2x+ cot x)
= cot x cot 2x - cot (2x+x)(cot 2x+ cot x)
[ as cot(A+B)=cotAcotB1cotAcotB]
= cot x cot 2x-(cot2xcotx1cotx+cot2x)(cot 2x+ cot x)
= cot x cot 2x- (cot 2x cot x-1)
= cot x cot 2x- cot 2x cot x+1
= 1
Hence, proved

1205010_1293652_ans_59f813163afc4c43a95abc5f1fa11d79.jpg

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