What is the value of cos(2arccos(0.5)) ?

The value of cos(2arccos(0.5)) is -1/2

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cos(2arccos(0.5))

cos (2 arccos (0.5))

- \frac{1}{2}

Solution steps

cos (2 arccos (0.5))

= cos (2 arccos (\frac{1}{2}))

Rewrite using trig identities:

2 cos^{2} (arccos (\frac{1}{2})) - 1

= 2 cos^{2} (arccos (\frac{1}{2})) - 1

Rewrite using trig identities:

cos (arccos (\frac{1}{2})) = \frac{1}{2}

= 2 (\frac{1}{2})^{2} - 1

Simplify

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

= - \frac{1}{2}

arcsin (\frac{1.52 \cdot sin ( 5 1 ^{\circ} )}{1.33})

\frac{20}{tan ( 1 5 ^{\circ} )}

cos (4 0^{\circ}) + cos (8 0^{\circ}) + cos (10 0^{\circ}) + cos (12 0^{\circ}) + cos (14 0^{\circ})

4 cos (π + \frac{π}{4})

2 sin (5 0^{\circ}) cos (5 0^{\circ})