Cosec teta/cosec teta-1+cosec teta/cosec teta+1=2sec^2teta
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cosecθ/cosecθ-1+cosecθ/cosecθ+1
l.h.s
do cross multiple
cosecθ(cosecθ+1)+(cosecθ-1)cosecθ/cosecθ^2-1
cosecθ^2+cosecθ+cosecθ^2-cosecθ/cosecθ^2-1
cosecθ^2+cosecθ^2/cosecθ^2-1
2cosecθ^2/cot^2θ
2(1/SIN^२θ)/COS^२θ/SIN^२θ
2(1/SIN^२θ)(COS^२θ/SIN^२θ)
2(1/COS^२θ)
2SEC^2θ
l.h.s
do cross multiple
cosecθ(cosecθ+1)+(cosecθ-1)cosecθ/cosecθ^2-1
cosecθ^2+cosecθ+cosecθ^2-cosecθ/cosecθ^2-1
cosecθ^2+cosecθ^2/cosecθ^2-1
2cosecθ^2/cot^2θ
2(1/SIN^२θ)/COS^२θ/SIN^२θ
2(1/SIN^२θ)(COS^२θ/SIN^२θ)
2(1/COS^२θ)
2SEC^2θ
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↑Above is the required answer :)
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