What is the value of (cos(30))/(sin(60)+cos(45)) ?

The value of (cos(30))/(sin(60)+cos(45)) is 3-sqrt(6)

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(cos(30))/(sin(60)+cos(45))

\frac{cos ( 3 0 ^{\circ} )}{sin ( 6 0 ^{\circ} ) + cos ( 4 5 ^{\circ} )}

3 - 6

Solution steps

\frac{cos ( 3 0 ^{\circ} )}{sin ( 6 0 ^{\circ} ) + cos ( 4 5 ^{\circ} )}

Use the following trivial identity:

cos (3 0^{\circ}) = \frac{3}{2}

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

= \frac{\frac{3}{2}}{\frac{3}{2} + \frac{2}{2}}

Simplify

\frac{\frac{3}{2}}{\frac{3}{2} + \frac{2}{2}} : 3 - 6

= 3 - 6

6 (cos (\frac{π}{2}) + i sin (\frac{π}{2}))

cos^{2} (0) - 3 sin (0)

arccos (\frac{( 20 ) ^{2} + ( 45 ) ^{2} - ( 53 ) ^{2}}{2 \cdot 20 \cdot 45})

arctan (\frac{4}{- 3}) + π

arccos (0.272)

What is the value of (cos(30))/(sin(60)+cos(45)) ?
The value of (cos(30))/(sin(60)+cos(45)) is 3-sqrt(6)