Question

(cosec A - cot A )² = 1 - cos A / 1 + cos A

Answer 1

since sin²A = 1- cos²A

Answer 2

Solution:

RHS = (cosecA-cotA)²

= [(1/sinA)-(cosA/sinA)]²

/*

i ) cosecA = 1/sinA

ii ) cotA = cosA/sinA */

= [ (1-cosA)/sinA ]²

= (1-cosA)²/sin²A

= (1-cosA)²/(1-cos²A)

/*

sin²A = 1- cos²A */

= (1-cosA)²/[(1+cosA)(1-cosA)]

/* we know the algebraic identity,

a²-b² = (a+b)(a-b) */

After cancellation, we get

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

= RHS

Therefore,

(cosec A-cot A)²=(1-cos A)/ (1+ cos A)

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