What is the general solution for arccos(x)=arcsin(9/41) ?

The general solution for arccos(x)=arcsin(9/41) is x= 40/41

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arccos(x)=arcsin(9/41)

arccos (x) = arcsin (\frac{9}{41})

x = \frac{40}{41}

Solution steps

arccos (x) = arcsin (\frac{9}{41})

Apply trig inverse properties

arccos (x) = arcsin (\frac{9}{41})

arccos (x) = a \Rightarrow x = cos (a)

x = cos (arcsin (\frac{9}{41}))

cos (arcsin (\frac{9}{41})) = \frac{40}{41}

cos (arcsin (\frac{9}{41}))

Rewrite using trig identities:

cos (arcsin (\frac{9}{41})) = 1 - (\frac{9}{41})^{2}

Use the following identity:

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

= 1 - (\frac{9}{41})^{2}

= 1 - (\frac{9}{41})^{2}

Simplify

= \frac{40}{41}

x = \frac{40}{41}

x = \frac{40}{41}

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What is the general solution for arccos(x)=arcsin(9/41) ?
The general solution for arccos(x)=arcsin(9/41) is x= 40/41