What is the value of cos(2arccos(0)) ?

The value of cos(2arccos(0)) is -1

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cos(2arccos(0))

cos (2 arccos (0))

- 1

Solution steps

cos (2 arccos (0))

Rewrite using trig identities:

2 cos^{2} (arccos (0)) - 1

cos (2 arccos (0))

Use the Double Angle identity:

cos (2 x) = 2 cos^{2} (x) - 1

= 2 cos^{2} (arccos (0)) - 1

= 2 cos^{2} (arccos (0)) - 1

Rewrite using trig identities:

cos (arccos (0)) = 0

Use the following identity:

cos (arccos (x)) = x

= 0

= 2 \cdot 0^{2} - 1

Simplify

= - 1

- 2 cos (2)

sin (2 arcsin (\frac{1}{3}))

\frac{3}{2} sec (\frac{π}{3})

cot (- \frac{π}{12})

arcsin (\frac{2}{8})