Question

(cotA-cosecA)^=1-cosA/1+cosA​

Answer 1

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

Solution:

RHS = (cosec A-cot A)²

i ) cosecA = 1/sinA

ii ) cotA = cosA/sinA

= [(1/sinA)-(cosA/sinA)]²

= [ (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)

hence proved..

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