Find the Exact Value tan(arcsin(3/5)-arctan(1/4))

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

Simplify each term.

Evaluate $\arcsin (\frac{3}{5})$ .

$\tan (0.6435011 - \arctan (\frac{1}{4}))$

Evaluate $\arctan (\frac{1}{4})$ .

$\tan (0.6435011 - 1 \cdot 0.24497866)$

Multiply $- 1$ by $0.24497866$ .

$\tan (0.6435011 - 0.24497866)$

Subtract $0.24497866$ from $0.6435011$ .

$\tan (0.39852244)$

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.42105263 \dots$