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Question
Prove that: (1+cot A - cosecA)(1 + tan A+ secA) =2.
Solution
L.H.S:`(1+(cos A)/(sinA)-1/(sinA))(1+(sinA)/(cosA)+1/(cosA))`
=`((sinA+cosA-1)/sinA)((cosA+sinA+1)/(cos A))`
=`((sinA+cosA)^2-(1)^2)/(sin A. cos A)`
=`(sin^2A +cos^2A+2sinA.cosA-1)/(sinA.cosA)`
=`(1+2sinA.cosA-1)/(sinA.cosA)`
=2
Hence, L.H.S =R.H.S.
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