CarissaKuehl
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Find the exact value of the expression. Do not use a calculator.

sec 60° - sin 60°

attached are answer options, if you could show step by step that would be great.

Find the exact value of the expression Do not use a calculator sec 60 sin 60 attached are answer options if you could show step by step that would be great class=

Respuesta :

[tex]\bf sec(60^o)-sin(60^o)\qquad \begin{cases} sec(\theta)=\cfrac{1}{cos(\theta)}\\ ------------\\ sin(60^o)\implies \cfrac{\sqrt{3}}{2} \\ \quad \\ cos(60^o)\implies \cfrac{1}{2} \end{cases} \\ \quad \\ \quad \\ sec(60^o)-sin(60^o)\implies \cfrac{1}{cos(60^o)}-sin(60^o) \\ \quad \\ \cfrac{1}{\frac{1}{2}}-\cfrac{\sqrt{3}}{2}\implies \cfrac{1}{1}\cdot \cfrac{2}{1}-\cfrac{\sqrt{3}}{2}\implies 2-\cfrac{\sqrt{3}}{2} \\ \quad \\ \textit{our LCD will be "2", thus} \\ \quad \\ \cfrac{4-\sqrt{3}}{2}[/tex]

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