What is the value of tan(arccos(24/25)-arcsin(12/13)) ?

The value of tan(arccos(24/25)-arcsin(12/13)) is -253/204

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tan(arccos(24/25)-arcsin(12/13))

tan (arccos (\frac{24}{25}) - arcsin (\frac{12}{13}))

- \frac{253}{204}

Solution steps

tan (arccos (\frac{24}{25}) - arcsin (\frac{12}{13}))

Rewrite using trig identities:

\frac{tan ( arccos ( \frac{24}{25} ) ) - tan ( arcsin ( \frac{12}{13} ) )}{1 + tan ( arccos ( \frac{24}{25} ) ) tan ( arcsin ( \frac{12}{13} ) )}

= \frac{tan ( arccos ( \frac{24}{25} ) ) - tan ( arcsin ( \frac{12}{13} ) )}{1 + tan ( arccos ( \frac{24}{25} ) ) tan ( arcsin ( \frac{12}{13} ) )}

Rewrite using trig identities:

tan (arccos (\frac{24}{25})) = \frac{7}{24}

Rewrite using trig identities:

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

= \frac{\frac{7}{24} - \frac{12}{5}}{1 + \frac{7}{24} \cdot \frac{12}{5}}

Simplify

\frac{\frac{7}{24} - \frac{12}{5}}{1 + \frac{7}{24} \cdot \frac{12}{5}} : - \frac{253}{204}

= - \frac{253}{204}

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What is the value of tan(arccos(24/25)-arcsin(12/13)) ?
The value of tan(arccos(24/25)-arcsin(12/13)) is -253/204