Question

cos45°÷sec30°+cosec30​

Answer 1

$\sf given : - \frac{ \cos(45) }{ \sec(30) } + \csc(30)$

now lemme tell you the values of these ratios :

• cos45° = √2/2

• sec30° = 2/√3

• csc30° = 2

$\sf \therefore value \: of \: \frac{ \cos(45) }{ \sec(30) } + \csc(30) \\ \\ \sf = \large{\frac{ \frac{1}{ \sqrt{2} } }{ \frac{2}{ \sqrt{3}} } } + 2 \\ \\ \sf = \left( \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{2} \right) + 2 \\ \\ \sf = \frac{ \sqrt{3} }{2 \sqrt{2} } + 2 \\ \\ \sf = \frac{ \sqrt{3} + 4 \sqrt{2} }{2 \sqrt{2} } \\ \\ \sf rationalising \\ \\ \sf = \frac{ \sqrt{3} + 4 \sqrt{2} }{2 \sqrt{2} } \times \frac{2 \sqrt{2} }{2 \sqrt{2} } \\ \\ \sf = \frac{2 \sqrt{2} ( \sqrt{3} + 4 \sqrt{2} )}{2 \sqrt{2} \times 2 \sqrt{2} } \\ \\ \sf = \frac{2 \sqrt{6} + 16 }{8} \\ \\ \sf = \frac{2( \sqrt{6} + 8)}{8} \\ \\ \sf = \frac{ \sqrt{6} + 8}{4}$

if your question is $\sf \frac{ \cos(45) }{ \sec(30) + \csc(30) }$

then you can refer to the attachment