What is the value of cos(2*arccos(1)) ?

The value of cos(2*arccos(1)) is 1

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cos(2*arccos(1))

cos (2 \cdot arccos (1))

1

Solution steps

cos (2 arccos (1))

Rewrite using trig identities:

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

cos (2 arccos (1))

Use the Double Angle identity:

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

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

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

Rewrite using trig identities:

cos (arccos (1)) = 1

Use the following identity:

cos (arccos (x)) = x

= 1

= 2 \cdot 1^{2} - 1

Simplify

= 1

cos (3 0^{\circ}) 600

- sin (sin (1)) cos (1)

sec (\frac{- 11 π}{3})

sin (- \frac{4}{7})

\frac{1}{2 ( sin ( 1 ) + cos ( 1 ) )}