(sin θ +cos θ )(sec θ +cosec θ )= 2+sec θ cosec θ
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LHS = (sin A+ cos A)(secA+cosec A)
sinA×secA+sinA×cosec A+cosA×secA+cosA×cosec A
= tan A+1+1+cot A
= 2 +( tan A+1/tanA )
=2+ ( tan ^2 A+1÷tanA)
=2+sec^2A/ tanA
=2+sec^2A× cosA÷sin A
=2+sec A×cos A= RHS .
.....PROVED
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