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22.cot x cot 2x-cot 2x cot 3x-cot 3x cot x = 1 |
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Answer» 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 writecot3x 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 |
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