Prove that (sinθ + cosecθ)2 + (cosθ + secθ)2 = 7 + tan2θ + cot2θ
sin2θ + cosec2θ + 2sinθ + cosecθ + cos2θ + sec2θ + 2cosθ secθ.
1 + cosec2θ + 2 + 2 + sec2θ.
1 + 1 + cot2θ + 2 + 2 + 1 + tan2θ
7 + tan2θ + cot2θ.