What is the value of (sin(300)+cos(150))/(tan(120)+cot(240)) ?

The value of (sin(300)+cos(150))/(tan(120)+cot(240)) is 3/2

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(sin(300)+cos(150))/(tan(120)+cot(240))

\frac{sin ( 30 0 ^{\circ} ) + cos ( 15 0 ^{\circ} )}{tan ( 12 0 ^{\circ} ) + cot ( 24 0 ^{\circ} )}

\frac{3}{2}

Solution steps

\frac{sin ( 30 0 ^{\circ} ) + cos ( 15 0 ^{\circ} )}{tan ( 12 0 ^{\circ} ) + cot ( 24 0 ^{\circ} )}

Simplify

= \frac{- sin ( 30 0 ^{\circ} ) - cos ( 15 0 ^{\circ} )}{- tan ( 12 0 ^{\circ} ) - cot ( 24 0 ^{\circ} )}

cot (24 0^{\circ}) = cot (6 0^{\circ})

= \frac{- sin ( 30 0 ^{\circ} ) - cos ( 15 0 ^{\circ} )}{- tan ( 12 0 ^{\circ} ) - cot ( 6 0 ^{\circ} )}

Rewrite using trig identities:

sin (30 0^{\circ}) = 2 sin (15 0^{\circ}) cos (15 0^{\circ})

= \frac{- 2 sin ( 15 0 ^{\circ} ) cos ( 15 0 ^{\circ} ) - cos ( 15 0 ^{\circ} )}{- tan ( 12 0 ^{\circ} ) - cot ( 6 0 ^{\circ} )}

Use the following trivial identity:

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

Use the following trivial identity:

cos (15 0^{\circ}) = - \frac{3}{2}

Rewrite using trig identities:

tan (12 0^{\circ}) = - 3

Use the following trivial identity:

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

= \frac{- 2 \cdot \frac{1}{2} ( - \frac{3}{2} ) - ( - \frac{3}{2} )}{- ( - 3 ) - \frac{3}{3}}

Simplify

\frac{- 2 \cdot \frac{1}{2} ( - \frac{3}{2} ) - ( - \frac{3}{2} )}{- ( - 3 ) - \frac{3}{3}} : \frac{3}{2}

= \frac{3}{2}

sin (\frac{π}{4}) cos (\frac{π}{3}) - cos (\frac{π}{4}) sin (\frac{π}{3})

4983 \cdot cos (4 0^{\circ})

\frac{sin ( tan ( 12.4 \cdot 0 ) )}{6.2 \cdot 0}

arcsin (0.5) - e^{- 2 (0.5)}

\frac{( 2.68 \cdot 9.80665 )}{sin ( 7 5 ^{\circ} )}

What is the value of (sin(300)+cos(150))/(tan(120)+cot(240)) ?
The value of (sin(300)+cos(150))/(tan(120)+cot(240)) is 3/2