Question

solve it. and you will get 20 thanks from my side​

Answer 1

$</p><p>\huge{\fbox{\fbox{\red{QUESTION:)}}}}$

cot x cot 2x - cot 2x cot 3x - cot 3x cot x = 1

$</p><p>\huge{\fbox{\fbox{\blue{ANSWER:)}}}}$

LHS = cot x.cot 2x -cot 2x.cot 3x -cot 3x.cot x

2x + x = 3x

take both sides, cot

take both sides, cotcot(x + 2x) = cot3x

use the formula,

cot(A + B) = (cotA.cotB-1)/(cotA+CotB)

(cotx.cot2x -1)/(cotx+cot2x) = cot3x

cotx.cot2x -1 = cot3x(cotx+cot2x)

cotx.cot2x -1 = cot3x.cotx + cot3x.cot2x

cotxcot2x - cot2x.cot3x - cot3x.cotx = 1

Hence, proved

$\huge\green{THANK\:YOU:)}$