sinA-2 sin^3A÷2cos^3A-cosA=tanA
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Step-by-step explanation:
LHS= sinA-2 sin³A/2cos³A-cosA
=sinA(1-2sin²A)/cosA(2cos²A-1)
=sinA(1-2sin²A)/cosA(2(1-sin²A)-1)
[cos²A=1-sin²A]
=sinA(1-2sin²A))cosA(2-2sin²A-1)
=sinA(1-2sin²A))cosA(1-2sin²A)
[(1-2sin²A cancels]
=sinA/cosA
=tanA
=RHS.
Hence proved.
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