What is the value of cos(2arcsin(12/13)) ?

The value of cos(2arcsin(12/13)) is -119/169

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cos(2arcsin(12/13))

cos (2 arcsin (\frac{12}{13}))

- \frac{119}{169}

Solution steps

cos (2 arcsin (\frac{12}{13}))

Rewrite using trig identities:

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

= 2 cos^{2} (arcsin (\frac{12}{13})) - 1

Rewrite using trig identities:

cos (arcsin (\frac{12}{13})) = \frac{5}{13}

= 2 (\frac{5}{13})^{2} - 1

Simplify

2 (\frac{5}{13})^{2} - 1 : - \frac{119}{169}

= - \frac{119}{169}

\frac{( 1 - cos ( 4 4 ^{\circ} ) )}{4}

\frac{cos ( \frac{π}{6} )}{1 - sin ( \frac{π}{6} )}

23 (cos (- \frac{5 π}{3}) + i sin (- \frac{5 π}{3}))

- cos (1 7^{\circ})

arctan (\frac{0.016}{0.025})

What is the value of cos(2arcsin(12/13)) ?
The value of cos(2arcsin(12/13)) is -119/169