(cosA-sinA+1)/(cosA+sinA-1)=cosecA+cotA
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Sia ? 6 years, 2 months ago
{tex}L H S=\frac{\cos A-\sin A+1}{\cos A+\sin A-1}{/tex}
{tex}=\frac{\sin A(\cos A-\sin A+1)}{\sin A(\cos A+\sin A-1)}{/tex}
{tex}=\frac{\sin A \cos A-\sin ^{2} A+\sin A}{\sin A(\cos A+\sin A-1)}{/tex}
{tex}=\frac{\sin A \cos A+\sin A-\left(1-\cos ^{2} A\right)}{\sin A(\cos A+\sin A-1)}{/tex}
{tex}=\frac{\sin A(\cos A+1)-(1-\cos A)(1+\cos A)}{\sin A(\cos A+\sin A-1)}{/tex}
{tex}=\frac{(1+\cos A)(\sin A+\cos A-1)}{\sin A(\cos A+\sin A-1)}{/tex}
{tex}=\frac{(1+\cos A)(\sin A+\cos A-1)}{\sin A(\cos A+\sin A-1)}{/tex}
{tex}=\frac{1}{\sin A}+\frac{\cos A}{\sin A}{/tex}
= cos A + cot A = RHS
Proved
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