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| 1. |
Prove that cot(2)^A(secA-1/1+sinA)+sec(2)^A (sinA-1/1+secA)=0 |
| Answer» L.H.S. = {tex}{{{{\\cot }^2}{\\rm{A}}\\left( {\\sec {\\rm{A}} - 1} \\right)} \\over {\\left( {1 + \\sin {\\rm{A}}} \\right)}} +{{{{\\sec }^2}{\\rm{A}}\\left( {\\sin {\\rm{A}} - 1} \\right)} \\over {\\left( {1 + \\sec {\\rm{A}}} \\right)}}{/tex}= {tex}{{{{\\cot }^2}{\\rm{A}}\\left( {\\sec {\\rm{A}} - 1} \\right)} \\over {\\left( {1 + \\sin {\\rm{A}}} \\right)}} \\times {{1 - \\sin {\\rm{A}}} \\over {1 - \\sin {\\rm{A}}}} \\times {{\\sec {\\rm{A}} + 1} \\over {\\sec {\\rm{A}} + 1}} + {{{{\\sec }^2}{\\rm{A}}\\left( {\\sin {\\rm{A}} - 1} \\right)} \\over {\\left( {1 + \\sec {\\rm{A}}} \\right)}}{/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)}} + {{{{\\sec }^2}{\\rm{A}}\\left( {\\sin {\\rm{A}} - 1} \\right)} \\over {\\left( {1 + \\sec {\\rm{A}}} \\right)}}{/tex}= {tex}{{{{\\cot }^2}{\\rm{A}}{\\rm{.ta}}{{\\rm{n}}^2}{\\rm{A}}\\left( {1 - \\sin {\\rm{A}}} \\right)} \\over {{{\\cos }^2}{\\rm{A}}\\left( {1 + \\sec {\\rm{A}}} \\right)}} + {{{{\\sec }^2}{\\rm{A}}\\left( {\\sin {\\rm{A}} - 1} \\right)} \\over {\\left( {1 + \\sec {\\rm{A}}} \\right)}}{/tex}= {tex}{{{{\\sec }^2}{\\rm{A}}\\left( {1 - \\sin {\\rm{A}}} \\right)} \\over {\\left( {1 + \\sec {\\rm{A}}} \\right)}} - {{{{\\sec }^2}{\\rm{A}}\\left( {1 - \\sin {\\rm{A}}} \\right)} \\over {\\left( {1 + \\sec {\\rm{A}}} \\right)}}{/tex}= 0= R.H.S. | |