cot x. cot 2x - cot 2x cot 3x - cot 3x cot x = 1 prove that LHS=RHS
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Hi Shaidaalam,
L.H.S=cot x. cot 2x - cot 2x. cot3x - cot x. cot3x
=cot x. cot 2x - cot3x(cot 2x +cot x)
=cotx .cot 2x - cot (x+2x) .(cot 2x+ cot x) [we can write cot3x as cot(x+2x)]
=cotx.cot2x- {(cot x. cot 2x -1)/(cot x + cot 2x)}.(cot x + cot 2x) [since cot(a+b)=(cot a. cot b -1)/(cot b+cot a)]
=cot x. cot 2x -cot x. cot 2x +1
=1
=R.H.S
Hope it's help.
shaidaalam:
thank u for this I was trying to do it but was not getting till the conclusion .........
Yep
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