Prove that ( cosec A + cot A) ( 1- cos A) = sin A.
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Solution:
LHS = (cosecA+cotA)(1-cosA)
=[1/sinA+cosA/sinA](1-cosA)
=[(1+cosA)/sinA](1-cosA)
= [(1+cosA)(1-cosA)]/sinA
= (1-cos²A)/sinA
= sin²A/sinA
/* 1-cos²A = sin²A */
= sinA
= RHS
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