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| 1. |
1 + costhita + sinthita ÷ 1 + costhita - sinthita = 1 + sinthita ÷ costhita |
| Answer» L.H.S. = {tex}{{1 + \\sin \\theta + \\cos \\theta } \\over {1 + \\cos \\theta - \\sin \\theta }}{/tex}Dividing all terms by {tex}{\\cos \\theta }{/tex}= {tex}{{\\sec \\theta + \\tan \\theta + 1} \\over {\\sec \\theta + 1 - \\tan \\theta }}{/tex}= {tex}{{\\sec \\theta + \\tan \\theta + 1} \\over {\\sec \\theta - \\tan \\theta + 1}} \\times {{\\sec \\theta + \\tan \\theta } \\over {\\sec \\theta + \\tan \\theta }}{/tex}= {tex}{{\\left( {\\sec \\theta + \\tan \\theta + 1} \\right)\\left( {\\sec \\theta + \\tan \\theta } \\right)} \\over {\\left( {\\sec {\\theta ^2} - {{\\tan }^2}\\theta } \\right) + \\left( {\\sec \\theta + \\tan \\theta } \\right)}}{/tex}= {tex}{{\\left( {\\sec \\theta + \\tan \\theta + 1} \\right)\\left( {\\sec \\theta + \\tan \\theta } \\right)} \\over {\\left( {1 + \\sec \\theta + \\tan \\theta } \\right)}}{/tex}= {tex}\\sec \\theta + \\tan \\theta {/tex}= {tex}{1 \\over {\\cos \\theta }} + {{\\sin \\theta } \\over {\\cos \\theta }}{/tex}= {tex}{{1 + \\sin \\theta } \\over {\\cos \\theta }}{/tex}R.H.S. | |