What is the value of cos(2arcsin(3/5)) ?

The value of cos(2arcsin(3/5)) is 7/25

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cos(2arcsin(3/5))

cos (2 arcsin (\frac{3}{5}))

\frac{7}{25}

Solution steps

cos (2 arcsin (\frac{3}{5}))

Rewrite using trig identities:

1 - 2 sin^{2} (arcsin (\frac{3}{5}))

= 1 - 2 sin^{2} (arcsin (\frac{3}{5}))

Rewrite using trig identities:

sin (arcsin (\frac{3}{5})) = \frac{3}{5}

= 1 - 2 (\frac{3}{5})^{2}

Simplify

1 - 2 (\frac{3}{5})^{2} : \frac{7}{25}

= \frac{7}{25}

tan (- 33 0^{\circ})

arctan (e^{0})

tan (4 π)

arccos (- \frac{4}{5})

tan (- 22 5^{\circ})