Question

Prove that (1+cos A)(1-cosA)(1+cot^2A)=1
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Answer 1

[ 1 + cos(a) ].[ 1 - cos(a) ].[ 1 + cot²(a) ] ------> LHS

[ 1 - cos²(a) ].[ 1 + cos²(a) / sin²(a) ]

[ 1 - cos²(a) ].[ sin²(a) + cos²(a) ] / sin²(a)

sin²(a) / sin²(a)

1

This is because, 1 - cos²(a) = sin²(a)

Hence proved.