Prove that (1+cot theta-cosec theta)(1+tan theta+sec theta)=2
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Expanding the expression given gives,
1 + cot theta - csc theta + tan theta + cot theta · tan theta - csc theta · tan theta + sec theta + cot theta · sec theta - csc theta · sec theta
= 1 + sin theta/cos theta - 1/cos theta + sin theta/cos theta + 1 - 1/sec theta · sin theta/cos theta + 1/cos theta + (sin theta/cos theta) · 1/cos theta - 1/sin theta · cos theta
= 2
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