Question

1+cot^2 a/1+cosec a = cosec a​

Answer 1

Given that :-

LHS = 1 + (Cot²A) / (1+CosecA)

So ,

= {1 +CosecA + Cot²A} / ( 1+ CosecA)

On multiplying Numerator & denominator by ( (1- CosecA)

= {( 1+CosecA +Cot²A) ( 1-CosecA)} / (1-Cosec²A)

= (1+CosecA+Cot²A-CosecA -Cosec²A -Cot²A.CosecA) / (1-Cosec²A)

We know that,

Cot²A+1 = Cosec²A

So ,

DENOMINATOR = 1-Cosec²A= -Cot²A

And NUMERATOR = 1+Cot²A-Cosec²A-Cot²A.CosecA

= Cosec²A-Cosec²A - Cot²A.CosecA

= -Cot²A.CosecA

Now, LHS = (-Cot²A.CosecA)/(-Cot²A)

= CosecA= RHS