tan(arccos(0.95))-tan(arccos(0.8))

Solución

tan (arccos (0.95)) - tan (arccos (0.8))

\frac{39}{19} - \frac{3}{4}

Notación decimal

- 0.42131 \dots

Pasos de solución

tan (arccos (0.95)) - tan (arccos (0.8))

= tan (arccos (\frac{19}{20})) - tan (arccos (\frac{4}{5}))

Re-escribir usando identidades trigonométricas:

tan (arccos (\frac{19}{20})) = \frac{1 - ( \frac{19}{20} ) ^{2}}{( \frac{19}{20} )}

Usar la siguiente identidad:

tan (arccos (x)) = \frac{1 - x ^{2}}{x}

= \frac{1 - ( \frac{19}{20} ) ^{2}}{( \frac{19}{20} )}

= \frac{1 - ( \frac{19}{20} ) ^{2}}{\frac{19}{20}} - tan (arccos (\frac{4}{5}))

Simplificar

= \frac{39}{19} - tan (arccos (\frac{4}{5}))

Re-escribir usando identidades trigonométricas:

tan (arccos (\frac{4}{5})) = \frac{3}{4}

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

Re-escribir usando identidades trigonométricas:

tan (arccos (\frac{4}{5})) = \frac{1 - ( \frac{4}{5} ) ^{2}}{( \frac{4}{5} )}

Usar la siguiente identidad:

tan (arccos (x)) = \frac{1 - x ^{2}}{x}

= \frac{1 - ( \frac{4}{5} ) ^{2}}{( \frac{4}{5} )}

= \frac{1 - ( \frac{4}{5} ) ^{2}}{\frac{4}{5}}

Simplificar

= \frac{3}{4}

= \frac{39}{19} - \frac{3}{4}

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