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

The value of (cos(45)*cos(30)+sin(45)*sin(60))/(tan(30)*tan(60)) is sqrt(3/2)

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

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

\frac{3}{2}

Solution steps

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

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

tan (3 0^{\circ}) = \frac{3}{3}

Use the following trivial identity:

tan (6 0^{\circ}) = 3

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

Simplify

\frac{\frac{2}{2} \cdot \frac{3}{2} + \frac{2}{2} \cdot \frac{3}{2}}{\frac{3}{3} 3} : \frac{3}{2}

= \frac{3}{2}

- 4 cos (2)

371 \cdot cos (9 0^{\circ} - 4 5^{\circ}) + 695.1 cos (4 5^{\circ})

sin (5) π^{\circ}

600 cosh (\frac{0}{600})

- 2 sinh (1 - 2)

What is the value of (cos(45)*cos(30)+sin(45)*sin(60))/(tan(30)*tan(60)) ?
The value of (cos(45)*cos(30)+sin(45)*sin(60))/(tan(30)*tan(60)) is sqrt(3/2)