Question

Solve cos45/sec30+cosec30

Answer 1

 Evaluate the following : (iii) " cos 45 " /"sec 30 + cosec 30 " We know that, " cos 45 " = 1/ 2 "sec 30 " = 1/(cos 30 ) = 1/( 3/2)  ...

Answer 2

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