What is the value of ((320/3))/((sin(30)+cos(30))) ?

The value of ((320/3))/((sin(30)+cos(30))) is -(320(1-sqrt(3)))/3

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((320/3))/((sin(30)+cos(30)))

\frac{( \frac{320}{3} )}{( sin ( 3 0 ^{\circ} ) + cos ( 3 0 ^{\circ} ) )}

- \frac{320 ( 1 - 3 )}{3}

Solution steps

\frac{( \frac{320}{3} )}{( sin ( 3 0 ^{\circ} ) + cos ( 3 0 ^{\circ} ) )}

= \frac{\frac{320}{3}}{sin ( 3 0 ^{\circ} ) + cos ( 3 0 ^{\circ} )}

Use the following trivial identity:

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

Use the following trivial identity:

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

= \frac{\frac{320}{3}}{\frac{1}{2} + \frac{3}{2}}

Simplify

\frac{\frac{320}{3}}{\frac{1}{2} + \frac{3}{2}} : - \frac{320 ( 1 - 3 )}{3}

= - \frac{320 ( 1 - 3 )}{3}

sin (6 0^{\circ}) - tan (4 5^{\circ})

(4 cos (3 0^{\circ}))^{2}

\frac{tan ( 0 )}{sec ( 0 )}

tan (37. 5^{\circ})

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

What is the value of ((320/3))/((sin(30)+cos(30))) ?
The value of ((320/3))/((sin(30)+cos(30))) is -(320(1-sqrt(3)))/3