Question

prove that :
coseco
coseco -1
+-
coseco
== 2 sec?0.
coseco +1​

Answer 1

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Answer 2

(Cosec ÷ (Cosec - 1)) + (Cosec ÷ (Cosec + 1)) = 2 Sec^2

L.H.S.,

= (Cosec ÷ (Cosec - 1)) + (Cosec ÷ (Cosec + 1))

= {(Cosec × (Cosec + 1)) + (Cosec × (Cosec - 1))} ÷ {(Cosec - 1) × (Cosec + 1)}

= (Cosec^2 + Cosec + Cosec^2 - Cosec) ÷ Cosec^2 - 1

= 2Cosec^2 ÷ (Cosec^2 - 1)

= 2Cosec^2 ÷ ((1÷Sin^2) -1)

= 2Cosec^2 ÷ ((1 - Sin^2) ÷ Sin^2)

= 2Cosec^2 × Sin^2 ÷ (1 - Sin^2)

= (2(1 ÷ Sin^2) × Sin^2) ÷ (1 - Sin^2)

= ((2 ÷ Sin^2) × Sin^2) ÷ (1 - Sin^2)

= 2 ÷ (1 - Sin^2)

Sorry but I can't tell you more I have reached till here please check it.