MATHEMATICS
cot x cot 2x - cot 2x cot 3x - cot 3x cot x = 1
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Answer:
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)=
cotAcotB
cotAcotB−1
]
= cot x cot 2x-(
cotx+cot2x
cot2xcotx−1
)(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
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