What is the value of (sin(120))/(tan(45)+sin(210)cos(300)) ?

The value of (sin(120))/(tan(45)+sin(210)cos(300)) is (2sqrt(3))/3

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(sin(120))/(tan(45)+sin(210)cos(300))

\frac{sin ( 12 0 ^{\circ} )}{tan ( 4 5 ^{\circ} ) + sin ( 21 0 ^{\circ} ) cos ( 30 0 ^{\circ} )}

\frac{2 3}{3}

Solution steps

\frac{sin ( 12 0 ^{\circ} )}{tan ( 4 5 ^{\circ} ) + sin ( 21 0 ^{\circ} ) cos ( 30 0 ^{\circ} )}

Rewrite as

= sin (21 0^{\circ}) cos (30 0^{\circ}) + tan (4 5^{\circ})

Rewrite using trig identities:

sin (21 0^{\circ}) cos (30 0^{\circ}) = \frac{sin ( 15 0 ^{\circ} ) - sin ( 9 0 ^{\circ} )}{2}

= \frac{sin ( 12 0 ^{\circ} )}{\frac{s i n ( 15 0 ^{\circ} ) - s i n ( 9 0 ^{\circ} )}{2} + tan ( 4 5 ^{\circ} )}

Simplify

= \frac{2 sin ( 12 0 ^{\circ} )}{sin ( 15 0 ^{\circ} ) - sin ( 9 0 ^{\circ} ) + 2 tan ( 4 5 ^{\circ} )}

Use the following trivial identity:

sin (12 0^{\circ}) = \frac{3}{2}

Use the following trivial identity:

sin (15 0^{\circ}) = \frac{1}{2}

Use the following trivial identity:

sin (9 0^{\circ}) = 1

Use the following trivial identity:

tan (4 5^{\circ}) = 1

= \frac{2 \cdot \frac{3}{2}}{\frac{1}{2} - 1 + 2 \cdot 1}

Simplify

\frac{2 \cdot \frac{3}{2}}{\frac{1}{2} - 1 + 2 \cdot 1} : \frac{2 3}{3}

= \frac{2 3}{3}

arccos (- \frac{1}{8})

10.3 sin (3 7^{\circ})

2 sin^{2} (\frac{3 π}{2})

sin (- 1 (- 1))

2 arctan (3)

What is the value of (sin(120))/(tan(45)+sin(210)cos(300)) ?
The value of (sin(120))/(tan(45)+sin(210)cos(300)) is (2sqrt(3))/3