Question

Cos45/
sec30+cosec30
​

Answer 1

Hlo

here is the solution

from the trignometric ratios cos45=1/root 2

sec30=2/root3

cose

HERE IT IS

Answer 2

$\huge\tt\red{\frac{ \cos45° }{ \sec30° + \cosec30° }}$

$\longrightarrow$$\huge\tt\purple{\frac{ \frac{1}{ \sqrt{2} } }{ \frac{2}{ \sqrt{3} } + 2 }}$

$\longrightarrow$$\huge\tt\purple{ \frac{ \frac{1}{2} }{ \frac{2 + 2 \sqrt{3} }{ \sqrt{3} } } }$

$\longrightarrow$$\huge\tt\purple{ \frac{ \sqrt{3} }{ \sqrt{2(2 + 2 \sqrt{3}) } } }$

$\longrightarrow$$\huge\tt\purple{\frac{ \sqrt{3} }{2 \sqrt{2} + 2 \sqrt{6} } }$

$\longrightarrow$$\huge\tt\purple{\frac{ \sqrt{3(2 \sqrt{6} - 2 \sqrt{2}) } }{(2 \sqrt{6} + 2 \sqrt{2} )(2 \sqrt{6} - 2 \sqrt{2} ) } }$

$\longrightarrow$$\huge\tt\purple{ \frac{2 \sqrt{3}( \sqrt{6} - \sqrt{2}) }{ {(2 \sqrt{6} )}^{2} - {(2 \sqrt{2} )}^{2} } }$

$\longrightarrow$$\huge\tt\purple{\frac{2 \sqrt{3}( \sqrt{6} - \sqrt{2} )}{24 - 8} }$

$\longrightarrow$$\huge\tt\purple{ \frac{2 \sqrt{3}( \sqrt{6} - \sqrt{2} ) }{16} }$

$\longrightarrow$$\huge\tt\purple{\frac{ \sqrt{18} - \sqrt{6} }{8} }$

$\longrightarrow$$\huge\tt\purple{\frac{3 \sqrt{2} - \sqrt{6} }{8} }$