Question

Prove that is here20%7B2%7D%20a" id="TexFormula1" title="1 - cos {2}a \div 1 - sin a{2} = tan {2} a" alt="1 - cos {2}a \div 1 - sin a{2} = tan {2} a" align="absmiddle" class="latex-formula">
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Answer 1

$\\ \sf\longmapsto \dfrac{1-cos2A}{1-sin2A}$

LHS

$\boxed{\sf \dfrac{cosA}{sinA}=cotA}$

$\\ \sf\longmapsto \dfrac{1-cos2A}{1-sin2A}$

$\\ \sf\longmapsto 1-cot2A$

$\\ \sf\longmapsto 1-\dfrac{1}{tan2A}$

$\\ \sf\longmapsto \dfrac{tan2A-1}{tan2A}$

$\\ \sf\longmapsto tan2A$