Question

(cosec a-cot a)= 1-cos a/1+cos a​

Answer 1

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



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