What is the value of (sin(30)+cos(330))/(tan(45)+cos(210)) ?

The value of (sin(30)+cos(330))/(tan(45)+cos(210)) is 5+3sqrt(3)

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(sin(30)+cos(330))/(tan(45)+cos(210))

\frac{sin ( 3 0 ^{\circ} ) + cos ( 33 0 ^{\circ} )}{tan ( 4 5 ^{\circ} ) + cos ( 21 0 ^{\circ} )}

5 + 33

Solution steps

\frac{sin ( 3 0 ^{\circ} ) + cos ( 33 0 ^{\circ} )}{tan ( 4 5 ^{\circ} ) + cos ( 21 0 ^{\circ} )}

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

Rewrite using trig identities:

cos (33 0^{\circ}) = \frac{3}{2}

Use the following trivial identity:

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

Rewrite using trig identities:

cos (21 0^{\circ}) = - \frac{3}{2}

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

Simplify

\frac{\frac{1}{2} + \frac{3}{2}}{1 - \frac{3}{2}} : 5 + 33

= 5 + 33

2 \cdot cos (\frac{π}{2})

7 sin (\frac{2 π}{3})

tan (\frac{2 π}{6})

cos (4.5)

10 sin (4 8^{\circ})

What is the value of (sin(30)+cos(330))/(tan(45)+cos(210)) ?
The value of (sin(30)+cos(330))/(tan(45)+cos(210)) is 5+3sqrt(3)