Question

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please try to solve

Answer 1

SOLUTION ☺️

The given trigonometric expression is:

$\frac{cos45}{sec30 + cosec30} \\ \\ = \frac{1 \div \sqrt{2} }{2 \div \sqrt{3} + 2} \\ \\ = \frac{1}{ \sqrt{2} } \times \frac{1}{2 + 2 \sqrt{3} \div \sqrt{3} } \\ \\ = \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{2(1 + \sqrt{ 3)} } \\ \\ = retioalizing \: the \: denominator \\ = \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } \times \frac{ \sqrt{3} }{2(1 + \sqrt{3)} } \times \frac{(1 - \sqrt{3)} }{(1 - \sqrt{3)} } \\ \\ = \frac{ \sqrt{2} }{2} \times \frac{ \sqrt{3} }{2} \times \frac{(1 - \sqrt{ 3)} }{(1 - 3)} \\ \\ = \frac{ \sqrt{6} }{4} \times \frac{(1 - \sqrt{3)} }{ - 2} \\ \\ = - \frac{ \sqrt{6} - 3 \sqrt{2} }{8} \\ \\ = \frac{3 \sqrt{2} - \sqrt{6} }{8}$

hope it helps ✔️

Answer 2

Hope it's helpful for you