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

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

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cos(2arccos(1))

cos (2 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

sin (\frac{11 π}{6}) + cos (\frac{5 π}{3})

2 cos (\frac{π}{2}) - (\frac{π}{2})

2 (sin (3 0^{\circ})) - tan (4 5^{\circ})

3 + 2 sin (\frac{π}{2})

sin (arcsin (\frac{12}{13}) + arcsin (\frac{4}{5}))