What is the value of tan(arcsin(3/4)-arccos(1/3)) ?

The value of tan(arcsin(3/4)-arccos(1/3)) is -(27sqrt(7)-32sqrt(2))/(65)

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tan(arcsin(3/4)-arccos(1/3))

tan (arcsin (\frac{3}{4}) - arccos (\frac{1}{3}))

- \frac{27 7 - 32 2}{65}

Solution steps

tan (arcsin (\frac{3}{4}) - arccos (\frac{1}{3}))

Rewrite using trig identities:

\frac{tan ( arcsin ( \frac{3}{4} ) ) - tan ( arccos ( \frac{1}{3} ) )}{1 + tan ( arcsin ( \frac{3}{4} ) ) tan ( arccos ( \frac{1}{3} ) )}

= \frac{tan ( arcsin ( \frac{3}{4} ) ) - tan ( arccos ( \frac{1}{3} ) )}{1 + tan ( arcsin ( \frac{3}{4} ) ) tan ( arccos ( \frac{1}{3} ) )}

Rewrite using trig identities:

tan (arcsin (\frac{3}{4})) = \frac{3 7}{7}

Rewrite using trig identities:

tan (arccos (\frac{1}{3})) = 22

= \frac{\frac{3 7}{7} - 2 2}{1 + \frac{3 7}{7} \cdot 2 2}

Simplify

\frac{\frac{3 7}{7} - 2 2}{1 + \frac{3 7}{7} \cdot 2 2} : - \frac{27 7 - 32 2}{65}

= - \frac{27 7 - 32 2}{65}

sin (15 6^{\circ})

\frac{sin ( 1 )}{1 - sin ( 1 )}

52 cos (\frac{π}{4})

arctan (\frac{12}{35})

sin (arcsin (\frac{π}{4}))

What is the value of tan(arcsin(3/4)-arccos(1/3)) ?
The value of tan(arcsin(3/4)-arccos(1/3)) is -(27sqrt(7)-32sqrt(2))/(65)