Question

plz help me to solve this

Answer 1

I hope this is the correct answer

Answer 2

Here is the solution

$= \frac{cos45}{sec30+cosec30}$

$= \frac{cos45}{ \frac{1}{cos30} + \frac{1}{sin30} }$

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

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

$= \frac{1}{ \sqrt{2} } * \frac{ \sqrt{3} }{2+2 \sqrt{3} }$

$= \frac{ \sqrt{3} }{2 \sqrt{2} +2 \sqrt{6} }$

$= \frac{1}{2}[ \frac{ \sqrt{3} }{ \sqrt{2} + \sqrt{6} }]$

$= \frac{1}{2}[ \frac{ \sqrt{3} }{ \sqrt{2} + \sqrt{6} }* \frac{\sqrt{2} - \sqrt{6}}{\sqrt{2} - \sqrt{6}} ]$

$= \frac{1}{2}[ \frac{ \sqrt{6}-3 \sqrt{2} }{ 2-6 } ]$

$= \frac{ 3 \sqrt{2}-\sqrt{6} }{ 8 }$