Question

cos 45°/sec 30° +cosec 30°​

Answer 1

Answer:

$\frac{ \frac{1}{2} }{ \frac{2}{ \sqrt{3} } } + 2 \\ = \frac{ \sqrt{3} }{4} + 2 \\ = \frac{ \sqrt{3} + 8}{4}$

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Answer 2

cos 45°/sec 30° + cosec 30°

$\frac{ \cos(45°) }{ \cos(30 °) + \cosec(30°) } \\ \\ = \frac{ \frac{1}{ \sqrt{2} } }{ \frac{2}{ \sqrt{3} } + 2 } \\ \\ = \frac{ \frac{1}{ \sqrt{2} } }{ \frac{2 + 2 \sqrt{3} }{ \sqrt{3} } } \\ \\ = \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{2(1 + \sqrt{3)} } \\ \\ = \frac{ \sqrt{2} }{ \sqrt{2} \times \sqrt{2} } \times \frac{ \sqrt{3} \times ( \sqrt{3} + 1)}{2( \sqrt{3 } + 1)( \sqrt{3} - 1)} \\ \\ = \frac{ \sqrt{6} ( \sqrt{3} - 1) }{4 \times (( \sqrt{3} ) {}^{2} - {1}^{2} )} \\ \\ = \frac{ \sqrt{6 } ( \sqrt{3} - 1)}{4 \times (3 - 1)} \\ \\ = \frac{ \sqrt{6} ( \sqrt{3} - 1) }{4(2)} \\ \\ = \frac{ \sqrt{6} ( \sqrt{3} - 1) }{8}$