What is the value of 1-2sin^2((5pi)/(12)) ?

The value of 1-2sin^2((5pi)/(12)) is 1-(2+sqrt(3))/2

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1-2sin^2((5pi)/(12))

1 - 2 sin^{2} (\frac{5 π}{12})

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

Solution steps

1 - 2 sin^{2} (\frac{5 π}{12})

Rewrite using trig identities:

sin (\frac{5 π}{12}) = \frac{6 + 2}{4}

= 1 - 2 (\frac{6 + 2}{4})^{2}

Simplify

1 - 2 (\frac{6 + 2}{4})^{2} : 1 - \frac{2 + 3}{2}

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

4 sin (\frac{1}{4})

\frac{tan ( \frac{π}{4} ) + tan ( \frac{π}{6} )}{1 - tan ( \frac{π}{4} ) tan ( \frac{π}{6} )}

arctan (\frac{13}{20})

sin (3 0^{\circ}) tan (4 5^{\circ}) + tan (3 0^{\circ}) sin (6 0^{\circ})

cos (arctan (- 3)) + csc (arcsec (2))

What is the value of 1-2sin^2((5pi)/(12)) ?
The value of 1-2sin^2((5pi)/(12)) is 1-(2+sqrt(3))/2