Question

Q55:what is the value of 1+cot
2x cot 3X+cot x cot 3x​

Answer 1

Answer:LHS = cotx.cot2x -cot2x.cot3x -cot3x.cotx

2x + x = 3x

take both sides, cot

cot(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 .

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