cos x cot 2x -cot2x cot3x -cot3x cotx=1
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Step-by-step explanation:
LHS = Cos x Cot 2x - cot 2x cot 3x - cot 3x cot x
= cot x cot 2x - cot 3x(cot2x + cotx)
= cot x cot 2x - cot (2x + x)(cot 2x + cot x)
( using Cot ( A+B)=
cot A cot B - 1
cot A + cot B )
cot x cot 2 x - ( cot 2xcot x-1)
( cot x + cot 2x ) ( cot 2x + cot x )
= cot x cot 2x - ( cot 2x cot x -1)
= cot x cot 2x - cot2x cot x +1
= 1 = RHS !!
HENCE PROVED !
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