Cot2 A ( sec A - 1 ) / 1 + sin A = sec2 A ( 1 - sin A ) / (1 + sec A )

1.	Cot2 A ( sec A - 1 ) / 1 + sin A = sec2 A ( 1 - sin A ) / (1 + sec A )
Answer» L.H.S. = {tex}{{{{\\cot }^2}{\\rm{A}}\\left( {\\sec {\\rm{A}} - 1} \\right)} \\over {1 + \\sin {\\rm{A}}}}{/tex}= {tex}{{{{\\cot }^2}{\\rm{A}}\\left( {\\sec {\\rm{A}} - 1} \\right)} \\over {1 + \\sin {\\rm{A}}}} \\times {{\\sec {\\rm{A}} + 1} \\over {\\sec {\\rm{A}} + 1}} \\times {{1 - \\sin {\\rm{A}}} \\over {1 - \\sin {\\rm{A}}}}{/tex}= {tex}{{{{\\cot }^2}{\\rm{A}}\\left( {{{\\sec }^2}{\\rm{A}} - 1} \\right)\\left( {1 - \\sin {\\rm{A}}} \\right)} \\over {\\left( {1 - {{\\sin }^2}{\\rm{A}}} \\right)\\left( {1 + \\sec {\\rm{A}}} \\right)}}{/tex}= {tex}{{{{\\cot }^2}{\\rm{A}}{\\rm{.}}{{\\tan }^2}{\\rm{A}}\\left( {1 - \\sin {\\rm{A}}} \\right)} \\over {{{\\cos }^2}A \\left( {1 + \\sec {\\rm{A}}} \\right)}}{/tex}= {tex}{{{{\\sec }^2}{\\rm{A}}\\left( {1 - \\sin {\\rm{A}}} \\right)} \\over {1 + \\sec {\\rm{A}}}}{/tex}= R.H.S.

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