What is the value of 2-4sin^2((5pi)/(12)) ?

The value of 2-4sin^2((5pi)/(12)) is -sqrt(3)

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2-4sin^2((5pi)/(12))

2 - 4 sin^{2} (\frac{5 π}{12})

- 3

Solution steps

2 - 4 sin^{2} (\frac{5 π}{12})

Rewrite using trig identities:

sin^{2} (\frac{5 π}{12}) = \frac{1 - cos ( \frac{5 π}{6} )}{2}

= 2 - 4 \cdot \frac{1 - cos ( \frac{5 π}{6} )}{2}

2 - 4 \cdot \frac{1 - cos ( \frac{5 π}{6} )}{2} = 2 cos (\frac{5 π}{6})

= 2 cos (\frac{5 π}{6})

Use the following trivial identity:

cos (\frac{5 π}{6}) = - \frac{3}{2}

= 2 (- \frac{3}{2})

Simplify

2 (- \frac{3}{2}) : - 3

= - 3

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

arctan (3.7)

cos (2 \frac{5 π}{6})

cos (\frac{π}{9}) cos (\frac{7 π}{18}) - sin (\frac{π}{9}) sin (\frac{7 π}{18})

2 sin (5) cos (5)

What is the value of 2-4sin^2((5pi)/(12)) ?
The value of 2-4sin^2((5pi)/(12)) is -sqrt(3)