Prove that: (sinθ+cosecθ)²+(cosθ+secθ)²=7+tan²θ+cot²θ

To prove: (sinθ+cosecθ)²+(cosθ+secθ)²=7+tan²θ+cot²θ
Solution:
L.H.S.=(sinθ+cosecθ)²+(cosθ+secθ)²
=sin²θ+cosec²θ+2sinθ.cosecθ+cos²θ+sec²θ+2cosθ.secθ
=(sin²θ+cos²θ)+1+cot²θ+2+1+tan²θ+2
=1+6+tan²θ+cot²θ
=7+tan²θ+cot²θ
=R.H.S.