What is the value of cos^2(1/2 arccos(12/13)) ?

The value of cos^2(1/2 arccos(12/13)) is 25/26

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cos^2(1/2 arccos(12/13))

cos^{2} (\frac{1}{2} arccos (\frac{12}{13}))

\frac{25}{26}

Solution steps

cos^{2} (\frac{1}{2} arccos (\frac{12}{13}))

Simplify:

\frac{1}{2} arccos (\frac{12}{13}) = \frac{arccos ( \frac{12}{13} )}{2}

= cos^{2} (\frac{arccos ( \frac{12}{13} )}{2})

Rewrite using trig identities:

\frac{1 + cos ( arccos ( \frac{12}{13} ) )}{2}

= \frac{1 + cos ( arccos ( \frac{12}{13} ) )}{2}

Rewrite using trig identities:

cos (arccos (\frac{12}{13})) = \frac{12}{13}

= \frac{1 + \frac{12}{13}}{2}

Simplify

\frac{1 + \frac{12}{13}}{2} : \frac{25}{26}

= \frac{25}{26}

3 sin (9 0^{\circ})

cos (arcsin (- \frac{4}{5}))

2 \cdot sin (6 0^{\circ})

6 sin (0)

sinh (ln (3))

What is the value of cos^2(1/2 arccos(12/13)) ?
The value of cos^2(1/2 arccos(12/13)) is 25/26