Question

kindly solve the above question for 15 points​

Answer 1

Step-by-step explanation:

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Answer 2

$\color{red}\huge{\underline{\underline{\bf GIVEN\dag}}}$

• $\frac{5 \sin ^{2}30 \degree + \cos {}^{2} 45 \degree- 4 \tan ^{2} 30 \degree }{2 \sin30 \degree\cos30 \degree+ \tan45 \degree }$

$\color{red}\huge{\underline{\underline{\bf SOLUTION\dag}}}$

$\frac{5 \sin ^{2}30 \degree + \cos {}^{2} 45 \degree- 4 \tan ^{2} 30 \degree }{2 \sin30 \degree\cos30 \degree+ \tan45 \degree }$

$\implies \frac{5 ({ \frac{1}{2} })^{2} + {( \frac{1}{ \sqrt{2} } )}^{2} - 4 {( \frac{1}{ \sqrt{3} } )}^{2} }{2( \frac{1}{2})( \frac{ \sqrt{3} }{2}) + 1 }$

$\implies \frac{5 ({ \frac{1}{4} }) + {( \frac{1}{ 2 } )} - 4 {( \frac{1}{ 3} )} }{2( \frac{1}{2})( \frac{ \sqrt{3} }{2}) + 1 }$

$\implies \frac{ { \frac{5}{4} } + { \frac{1}{ 2 } } - {\frac{4}{ 3} } }{\frac{ \sqrt{3} }{2} + 1 }$

$\implies \frac{ { \frac{15 + 6 - 16}{12} } {{ } } }{\frac{ \sqrt{3} + 2}{2} }$

$\implies \frac{ { \frac{5}{6} } {{ } } }{ \sqrt{3} + 2}{}$

$\implies { \frac{5 }{6( \sqrt{3} + 2)} }$

$\red{\therefore \frac{5 }{6\sqrt{3}+12} }$