(cotA/2-tanA/2)=2cotA
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Step-by-step explanation:
Cot A/2-tan A/2= (cos A/2)/(sin A/2) - (sin A/2)/(cos A/2)
= {(cos A/2)² - (sin A/2)²} / (sin A/2 cos A/2)
= cos A / (sin A/2 cos A/2) ... half angle formula
= 2cosA / (2sin A/2 cos A/2) ... multiply divide by 2
= 2 cot A ... half angle formula
...thus proved
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