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| 1. |
Prove that tanA +sinA/tanA-sinA = secA +1/secA-1=1+cosA/1- cosA\xa0 |
| Answer» {tex}{{\\tan {\\rm{A}} + \\sin {\\rm{A}}} \\over {\\tan {\\rm{A}} - \\sin {\\rm{A}}}}{/tex}= {tex}{{{{\\sin {\\rm{A}}} \\over {\\cos {\\rm{A}}}} + \\sin {\\rm{A}}} \\over {{{\\sin {\\rm{A}}} \\over {\\cos {\\rm{A}}}} - \\sin {\\rm{A}}}}{/tex}= {tex}{{\\sin {\\rm{A}} + \\cos {\\rm{A}}.\\sin {\\rm{A}}} \\over {\\sin {\\rm{A}} - \\cos {\\rm{A}}.\\sin {\\rm{A}}}}{/tex}= {tex}{{\\sin {\\rm{A}}\\left( {1 + \\cos {\\rm{A}}} \\right)} \\over {\\sin {\\rm{A}}\\left( {1 - \\cos {\\rm{A}}} \\right)}}{/tex}= {tex}{{1 + \\cos {\\rm{A}}} \\over {1 - \\cos {\\rm{A}}}}{/tex}Proved.Also, {tex}{{1 + \\cos {\\rm{A}}} \\over {1 - \\cos {\\rm{A}}}}{/tex}= {tex}{{1 + {1 \\over {\\sec {\\rm{A}}}}} \\over {1 - {1 \\over {\\sec {\\rm{A}}}}}}{/tex}= {tex}{{\\sec {\\rm{A}} + 1} \\over {\\sec {\\rm{A}} - 1}}{/tex}Proved. | |