Question

prove that cot x - cot 2x = cosev 2x

Answer 1

to prove cotA - cot2A = csc2A

work on the LHS
cosA/sinA - cos2A/sin2A

use identities cos2A = 2cos²A-1 and sin2A = 2sinAcosA
cosA/sinA - (2cos²A - 1)/2sinAcosA

put under common denominator
(2cos²A - 2cos²A +1) /2sinAcosA

1 / sin2A

csc2A = RHS


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