Question

pls answer correctly ​

Answer 1

Answer:

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Answer 2

Answer:

According to your question , wr have to evalute the following by putting the value of Trignometery ratios

$\frac{5 \cos {}^{2} ( {60}^{ } ) + 4 {sec}^{2}30 - {tan}^{2} 45 }{sin {}^{2}30 + {cos}^{2} 30 } \\ \\ = \geqslant cos60 = \frac{1}{2} \\ \\ = \geqslant sec30 = \frac{2}{ \sqrt{3} } \\ \\ = \geqslant tan45 = 1 \\ \\ = \geqslant sin30 = \frac{1}{2} \\ \\ = \geqslant cos30 = \frac{ \sqrt{3} }{2} \\ \\ = \geqslant \frac{5cos {}^{2} 60 \: + 4 {sec}^{2} 30 - {tan}^{2}45 }{ {sin}^{2} 30 + {cos}^{2}30 } \\ \\ = \geqslant \frac{5 \times ( \frac{1}{2} ) {}^{2} + 4 \times ( \frac{2}{ \sqrt{3} } ) {}^{2} - (1) {}^{2} }{( \frac{1}{2} ) {}^{2} + ( \frac{ \sqrt{3} }{2} ) {}^{2} } \\ \\ = > \frac{5 \times \frac{1}{4} + 4 \times \frac{4}{3} - 1 }{ \frac{1}{4} + \frac{3}{4} } \\ \\ = \geqslant \frac{ \frac{5}{4} + \frac{16}{3} - 1 }{ \frac{1 + 3}{4} } \\ \\ = \geqslant \frac{ \frac{15 + 64}{12} - 1}{ \frac{4}{4} } \\ \\ = \geqslant \frac{ \frac{79}{12} - 1 }{1}$

$\frac{79}{12} - 1 \\ \\ = \geqslant \frac{79 - 12}{12} \\ \\ = \geqslant \frac{67}{12}$