Prove that
√sec θ−1sec θ+1+√sec θ+1sec θ−1=2 cosec θ
=2 cosec θ
√sec θ−1sec θ+1+√sec θ+1sec θ−1
=(√sec θ−1)2+(√sec θ+1)2√sec2 θ−12
=sec θ−1+sec θ+1√sec2 θ−1
=2 sec θ√tan2 θ
=2 sec θtan θ
=21cos θsin θcos θ
=2sin θ
=2 cosec θ