Answer:
L.H.S. \[=(sin\,\theta +cos\,\theta +1).(sin\,\theta -1+cos\,\theta ).sec\,\theta \text{ }.\text{ }cosec\text{ }\theta \] \[=[(\sin \theta +\cos \theta )+1].[(\sin \theta +\cos \theta )-1].\sec \theta .\cos ec\theta \] \[=[{{(\sin \theta +\cos \theta )}^{2}}-{{(1)}^{2}}]\sec \theta \,\,\cos ec\theta \] \[[\because \,\,(a+b)(a-b)={{a}^{2}}-{{b}^{2}}]\] \[=(2\,\,\sin \theta \cos \theta ).\frac{1}{\cos \theta }.\frac{1}{\sin \theta }\] \[=2=R.H.S.\] Hence Proved.
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