Question

prove that (1-cosA)(1+cosA)(1+cotA×cotA)=1

Answer 1

Heya!!
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◾( 1 - CosA ) ( 1 + CosA) ( 1 + CotA × CotA) = 1

Now , using the identity ( a - b ) (a + b ) = ( a² - b² )


=>> ( 1 - Cos²A ) ( 1 + Cot²A)

=>> Now,
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◀1 - Cos² A = Sin²A as

◀1 + Cot²A = Cosec²A


〰▪Putting in Values ,


( Sin²A ) ( Cosec²A)


=>>> Now, Sin²A = 1/ Cosec²A


We have !!
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( Sin²A ) × 1/ Sin²A


= 1 = RHS!!

Answer 2

( 1 - CosA ) ( 1 + Cos A ) ( 1 + CotA × CotA ) = 1

LHS = ( 1 - Cos A ) ( 1 + Cos A ) ( 1 + CotA × Cot )



=> ( 1 - Cos²A ) ( 1 + Cot²A )



=> Sin²A × Cosec²A



=> Sin²A × 1/ Sin²A


=> 1


Hence,

LHS = RHS = 1.