What is the value of (sin(30))/(sin(22.5)) ?

The value of (sin(30))/(sin(22.5)) is ((2+sqrt(2))sqrt(2-\sqrt{2)})/2

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(sin(30))/(sin(22.5))

\frac{sin ( 3 0 ^{\circ} )}{sin ( 22. 5 ^{\circ} )}

\frac{( 2 + 2 ) 2 - 2}{2}

Solution steps

\frac{sin ( 3 0 ^{\circ} )}{sin ( 22. 5 ^{\circ} )}

Use the following trivial identity:

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

Rewrite using trig identities:

sin (22. 5^{\circ}) = \frac{2 - 2}{2}

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

Simplify

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

= \frac{( 2 + 2 ) 2 - 2}{2}

\frac{cos ( \frac{π}{6} )}{- sin ( \frac{π}{6} )}

cos^{2} (\frac{3 π}{8}) + cos^{2} (\frac{π}{8})

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

tan^{2} (1921 4^{\circ})

arcsec (- 1.0167)

What is the value of (sin(30))/(sin(22.5)) ?
The value of (sin(30))/(sin(22.5)) is ((2+sqrt(2))sqrt(2-\sqrt{2)})/2