Question

show that cot2x cotx-cot3x cot 2x-cot 3x cot x=1

Answer 1

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