sin²30cos²45+4tan²30+1/2sin²90-2cos²+1/24cos²0 please simply

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Sia ? 6 years, 6 months ago
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}
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