Answer :

Given L.H.S. = (sin θ + cosec θ)2 + (cos θ + sec θ)2


We know




sin2 θ + cosec2 θ + 2 + cos2 θ + sec2 θ + 2


Also From the Trigonometrical identities


sin2θ + cos2θ = 1


cosec2 θ = 1 + cot2 θ


sec2 θ = 1 + tan2 θ


1 + 1 + cot2 θ + 2 + 1 + tan2 θ + 2


7 + cot2 θ + tan2 θ


So, L.H.S = R.H.S


Hence Proved


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