Question

Prove that 1-cosA/1+cosA = (cosecA-cosA)^2

Answer 1

Step-by-step explanation:

====================================

RHS

( cosecA - cotA )²

= ( 1/ sinA - cosA/sinA )²

= ( 1 - cosA/ sinA )²

= ( 1 + cosA )²/ sin²A

= ( 1 - cosA )²/ 1 - cos²A

= ( 1 - cosA ) ( 1 - cosA )/ ( 1 + cosA ) ( 1 - cosA )

= 1 - cosA / 1 + cosA

= LHS

hope this will help u......

Answer 2

Proof:

Consider the LHS of the given equation

(1 - CosA)/(1 + CosA)

Multiply and divide it with (1 - cosA)

(1 - CosA)/(1 + CosA) × (1 - cosA)/(1 - cosA)

On multiplying, we get

=> (1 - cos A)²/(1 - Cos²A)

=> (1 - cos A)²/sin²A               (because Sin²A + Cos²A = 1)

=> [ (1/sinA) - (cosA/SinA) ]²

=> [ CosecA - CotA ]²     ( because 1/sinA = Cosec A) & ( cos A / Sin A = Cot A)