cosec15°+sec15°=1sin15°+1cos15°=cos15°+sin15°sin15°cos15° =3+122+3−122sin30°2=3+1+3−12214=26

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$\cos e c 15 ° + \sec 15 ° =$

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\sqrt{6} + \sqrt{2}

\sqrt{6}

2 \sqrt{6}

2 \sqrt{2}

answer is C.

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Detailed Solution

\cos e c 15 ° + \sec 15 ° = \frac{1}{\sin 15 °} + \frac{1}{\cos 15 °} = \frac{\cos 15 ° + \sin 15 °}{\sin 15 ° \cos 15 °}

$= \frac{\frac{\sqrt{3} + 1}{2 \sqrt{2}} + \frac{\sqrt{3} - 1}{2 \sqrt{2}}}{\frac{\sin 30 °}{2}} = \frac{\frac{\sqrt{3} + 1 + \sqrt{3} - 1}{2 \sqrt{2}}}{\frac{1}{4}} = 2 \sqrt{6}$

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