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| 1. |
Tan5° tan25° tan30° tan65°tan85° =1/ root 3 |
| Answer» We have,tan 5° tan 25° tan 30° tan 65° tan 85°= (tan 5° tan 85°) (tan 25° tan 65°) tan 30° {tex}\\left[ \\begin{array} { c } { \\because \\tan 85 ^ { \\circ } = \\tan \\left( 90 ^ { \\circ } - 5 ^ { \\circ } \\right) = \\cot 5 ^ { \\circ } } \\\\ { \\tan 65 ^ { \\circ } = \\tan \\left( 90 ^ { \\circ } - 25 ^ { \\circ } \\right) = \\cot 25 ^ { \\circ } } \\end{array} \\right] {/tex}= (tan 5° cot 5°) (tan 25° cot 25°) tan 30°={tex}\\left(tan5^\\circ\\times\\frac1{\\tan5^\\circ}\\right)\\left(tan25^\\circ\\times\\frac1{\\tan25^\\circ}\\right){/tex}{tex}\\left[cot\\theta=\\frac1{\\tan\\theta}\\right]{/tex}{tex}= 1 \\times 1 \\times \\frac { 1 } { \\sqrt { 3 } } = \\frac { 1 } { \\sqrt { 3 } } {/tex} | |