What is the value of (sqrt(2-\sqrt{2+2cos(80))})/(sin(40)) ?

The value of (sqrt(2-\sqrt{2+2cos(80))})/(sin(40)) is 1.06417…

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(sqrt(2-\sqrt{2+2cos(80))})/(sin(40))

\frac{2 - 2 + 2 cos ( 8 0 ^{\circ} )}{sin ( 4 0 ^{\circ} )}

1.06417 \dots

Solution steps

\frac{2 - 2 + 2 cos ( 8 0 ^{\circ} )}{sin ( 4 0 ^{\circ} )}

Refine to a decimal form

= 1.06417 \dots

\frac{4}{sin ( 3 5 ^{\circ} )}

arctan (\frac{- 3.43}{1.1})

14 \cdot (cos (2 4^{\circ}))

- \frac{14 π}{3} sin (\frac{2 π ^{2.3} + 4 π}{3})

cos (14 0^{\circ}) cos (5 0^{\circ}) - sin (14 0^{\circ}) sin (5 0^{\circ})

What is the value of (sqrt(2-\sqrt{2+2cos(80))})/(sin(40)) ?
The value of (sqrt(2-\sqrt{2+2cos(80))})/(sin(40)) is 1.06417…