Prove that cotx cot2x cot2x cot3x cot3x cotx 1
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Question 22 Prove that cot x cot 2x – cot 2x cot 3x – cot 3x cot x = 1
Class X1 - Maths -Trigonometric Functions Page 74
Answered by admin @
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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