Question

Evaluate the work below​

Answer 1

Answer:

$3 \sqrt{2}$

Step-by-step explanation:

Given

$\frac{ \sin(60) \sec(60) \cot(30) }{ \cos( 45) ) }$

Using the unit circle, we know that

$\sin(60) = \frac{ \sqrt{3} }{2}$

$\cos(45) = \frac{ \sqrt{2} }{2}$

We can find sec and cot by using reciprocal identies.

$\sec(x) = \frac{1}{ \cos(x) }$

$\cos(60) = \frac{1}{2}$

So

$\sec(60) = 2$

$cot(x) = \frac{1}{ \tan(x) }$

$\tan(30) = \frac{1}{ \sqrt{3} }$

so

$\cot(30) = \sqrt{3}$

Plug in the values.

$\frac{ \frac{ \sqrt{3} }{2} \times 2 \times \sqrt{3} }{ \frac{ \sqrt{2} }{2} }$

$\frac{ \frac{ \sqrt{3} }{2} \times \frac{ \sqrt{12} }{1} }{ \frac{ \sqrt{2} }{2} }$

$\frac{3}{ \frac{ \sqrt{2} }{2} }$

$3 \sqrt{2}$