What is the value of tan(arcsin(3/4)-arccos(1/5)) ?

The value of tan(arcsin(3/4)-arccos(1/5)) is -(75sqrt(7)-32sqrt(6))/(209)

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tan(arcsin(3/4)-arccos(1/5))

tan (arcsin (\frac{3}{4}) - arccos (\frac{1}{5}))

- \frac{75 7 - 32 6}{209}

Solution steps

tan (arcsin (\frac{3}{4}) - arccos (\frac{1}{5}))

Rewrite using trig identities:

\frac{tan ( arcsin ( \frac{3}{4} ) ) - tan ( arccos ( \frac{1}{5} ) )}{1 + tan ( arcsin ( \frac{3}{4} ) ) tan ( arccos ( \frac{1}{5} ) )}

= \frac{tan ( arcsin ( \frac{3}{4} ) ) - tan ( arccos ( \frac{1}{5} ) )}{1 + tan ( arcsin ( \frac{3}{4} ) ) tan ( arccos ( \frac{1}{5} ) )}

Rewrite using trig identities:

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

Rewrite using trig identities:

tan (arccos (\frac{1}{5})) = 26

= \frac{\frac{3 7}{7} - 2 6}{1 + \frac{3 7}{7} \cdot 2 6}

Simplify

\frac{\frac{3 7}{7} - 2 6}{1 + \frac{3 7}{7} \cdot 2 6} : - \frac{75 7 - 32 6}{209}

= - \frac{75 7 - 32 6}{209}

- csc (\frac{7 π}{6})

tan (arccos (\frac{π}{2}))

arcsin (cos (- \frac{π}{6}))

\frac{tan ( 10 0 ^{\circ} ) - tan ( - 2 0 ^{\circ} )}{1 + tan ( 10 0 ^{\circ} ) tan ( - 2 0 ^{\circ} )}

sin (2 (4 0^{\circ}))

What is the value of tan(arcsin(3/4)-arccos(1/5)) ?
The value of tan(arcsin(3/4)-arccos(1/5)) is -(75sqrt(7)-32sqrt(6))/(209)