Question

Cos45/sec30+cosec30
Find this value please

Answer 1

Answer:

$\frac{ \cos(45) }{ \sec(30) + \cosec(30) } = \frac{ \frac{1}{ \sqrt{2} } }{ \frac{2 }{ \sqrt{3} } +2 } \\ = \frac{ \frac{1}{ \sqrt{2} } }{ \frac{2(1 + \sqrt{3} )}{ \sqrt{3} } } = \frac{ \sqrt{3} }{2 \sqrt{2}(1 + \sqrt{3} ) }$

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Answer 2

$\frac{cos45 \degree}{sec30 \degree + cosec30 \degree} \\ \\ = \frac{ \frac{1}{ \sqrt{2} } }{ \frac{2}{ \sqrt{3} } + 2 } \\ \\ = \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{ 2 + 2 \sqrt{3} } \\ \\ = \frac{ \sqrt{3} }{2 \sqrt{2} + 2 \sqrt{6} } \\ \\ = \frac{ \sqrt{3} }{2 \sqrt{2} + 2 \sqrt{6} } \times \frac{2 \sqrt{2} - 2 \sqrt{6} }{2 \sqrt{2} - 2 \sqrt{6} } \\ \\ = \frac{2 \sqrt{6} - 2 \sqrt{18} }{8 - 24} \\ \\ = \frac{2 \sqrt{6} - 6 \sqrt{2} }{ - 16} \\ \\ = \frac{3 \sqrt{2} - \sqrt{6} }{8}$