prove that cot x - cot 2x = cosev 2x
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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
this is your answer
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
this is your answer
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