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Cos45/sec30 +cosec30 |
| Answer» {tex} Value \\: of \\:\\frac{cos45}{(sec30+cosec30)}{/tex}{tex}=\\frac{\\frac{1}{\\sqrt{2}}}{\\frac{2}{\\sqrt{3}}+2}{/tex}{tex}=\\frac{\\frac{1}{\\sqrt{2}}}{\\frac{2+2\\sqrt{3}}{\\sqrt{3}}}{/tex}{tex}=\\frac{1}{\\sqrt{2}}\\times \\frac{\\sqrt{3}}{2(1+\\sqrt{3})}{/tex}{tex}=\\frac{\\sqrt{2}}{\\sqrt{2}\\times \\sqrt{2}} \\times \\frac{\\sqrt{3}\\times (\\sqrt{3}-1)}{2(\\sqrt{3}+1)(\\sqrt{3}-1)}{/tex}{tex}=\\frac{\\sqrt{6}(\\sqrt{3}-1)}{4\\left(\\big(\\sqrt{3}\\big)^{2}-1^{2}\\right)}{/tex}{tex}=\\frac{\\sqrt{6}(\\sqrt{3}-1)}{4(3-1)}{/tex}{tex}=\\frac{\\sqrt{6}(\\sqrt{3}-1)}{8}{/tex}Therefore,Value{tex} \\: of \\:\\frac{cos45}{(sec30+cosec30)}\\\\=\\frac{\\sqrt{6}(\\sqrt{3}-1)}{8}{/tex} | |