Question

cos 45º
sec 30° + cosec 60°​

Answer 1

Given,

$\[\cos 45^\circ \sec 30^\circ + \cos ec60^\circ \]$

Solution,

$\[ = \cos 45^\circ \sec 30^\circ + \cos ec60^\circ \]$

Put the values.

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

$\[ = \frac{2}{{\sqrt 3 }} \times \left( {\frac{1}{{\sqrt 2 }} + 1} \right)\]$

$\[ = \frac{2}{{\sqrt 3 }} \times \left( {\frac{{1 + \sqrt 2 }}{{\sqrt 2 }}} \right)\]$

$\[ = \sqrt {\frac{2}{3}} \times \left( {\sqrt 2 + 1} \right)\]$

Hence the value is $\[ \sqrt {\frac{2}{3}} \times \left( {\sqrt 2 + 1} \right)\]$