Prove that : sinA- 2sin^A / 2cos ^ A - cos A = tan A

1.	Prove that : sinA- 2sin^A / 2cos ^ A - cos A = tan A
Answer» LHS =\xa0{tex}\\frac{\\sin A-2 \\sin ^{3} A}{2 \\cos ^{3} A-\\cos A}{/tex}=\xa0{tex}\\frac{\\sin A\\left(1-2 \\sin ^{2} A\\right)}{\\cos A\\left(2 \\cos ^{2} A-1\\right)}{/tex}=\xa0{tex}\\frac{\\sin A\\left(1-2\\left(1-\\cos ^{2} A\\right)\\right)}{\\cos A\\left(2 \\cos ^{2} A-1\\right)}{/tex}\xa0[{tex}\\because sin^2\\theta=1-cos^2\\theta{/tex}]=\xa0{tex}\\frac{\\sin A\\left(1-2+2cos ^{2} A\\right)}{\\cos A\\left(2 \\cos ^{2} A-1\\right)}{/tex}=\xa0{tex}\\tan A \\frac{\\left(2 \\cos ^{2} A-1\\right)}{\\left(2 \\cos ^{2} A-1\\right)}{/tex}= tan A = RHSHence proved.

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