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| 1. |
sin²30cos²45+4tan²30+1/2sin²90-2cos²+1/24cos²0 please simply |
| Answer» We know that, Sin30°=(1/2), Cos45°=(1/√2), Sin90°=1, Cos90°=0, Cos0°=1 & tan30°=(1/√3), putting these values in the given expression, we get :-{tex}{\\sin ^2}30^\\circ {\\cos ^2}45^\\circ + 4{\\tan ^2}30^\\circ + \\;\\frac{1}{2}{\\sin ^2}90^\\circ - 2\\cos^2 90^\\circ + \\frac{1}{{24}}{\\cos ^2}0^\\circ {/tex}{tex} = {\\left( {\\frac{1}{2}} \\right)^2} \\times {\\left( {\\frac{1}{{\\sqrt 2 }}} \\right)^2} + 4{\\left( {\\frac{1}{{\\sqrt 3 }}} \\right)^2} + \\frac{1}{2} \\times {\\left( 1 \\right)^2} - 2 \\times {\\left( 0 \\right)^2} + \\frac{1}{{24}}{\\left( 1 \\right)^2}{/tex}{tex} = \\frac{1}{4} \\times \\frac{1}{2} + 4 \\times \\frac{1}{3} + \\frac{1}{2} \\times 1 - 2 \\times 0 + \\frac{1}{{24}} \\times 1{/tex}{tex} = \\frac{1}{8} + \\frac{4}{3} + \\frac{1}{2} - 0 + \\frac{1}{{24}}{/tex}{tex} = \\frac{{3 + 32 + 12 - 0 + 1}}{{24}}{/tex}{tex} = \\frac{{48}}{{24}} = 2{/tex} | |