Prove that (CosecA/CosecA-1)+(CosecA/CosecA+1)=2Sec^2A
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Step-by-step explanation:
LHS = (CosecA/CosecA-1)+(CosecA/CosecA+1)
= CosecA × [(1/CosecA-1)+(1/CosecA+1)]
= CosecA × (CosecA+1+CosecA-1)/[(CosecA-1)×(CosecA+1)]
= CosecA × 2CosecA/(Cosec²A-1)
= 2Cosec²A/Cot²A [∵Cosec²A-1=Cot²A]
= 2 Cosec²A tan²A
= 2 × 1/Sin²A × Sin²A/Cos²A
= 2×1/Cos²A
= 2Sec²A
= RHS [Proved]
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