What is the value of tan(pi+arcsin(2/3)) ?

The value of tan(pi+arcsin(2/3)) is (2sqrt(5))/5

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tan(pi+arcsin(2/3))

tan (π + arcsin (\frac{2}{3}))

\frac{2 5}{5}

Solution steps

tan (π + arcsin (\frac{2}{3}))

Rewrite using trig identities:

\frac{tan ( 0 ) + tan ( arcsin ( \frac{2}{3} ) )}{1 - tan ( 0 ) tan ( arcsin ( \frac{2}{3} ) )}

= \frac{tan ( 0 ) + tan ( arcsin ( \frac{2}{3} ) )}{1 - tan ( 0 ) tan ( arcsin ( \frac{2}{3} ) )}

Use the following trivial identity:

tan (0) = 0

Rewrite using trig identities:

tan (arcsin (\frac{2}{3})) = \frac{2 5}{5}

= \frac{0 + \frac{2 5}{5}}{1 - 0 \cdot \frac{2 5}{5}}

Simplify

= \frac{2 5}{5}

- sin^{2} (1)

20 tan (3 0^{\circ})

\frac{2}{tan ( 6 5 ^{\circ} )}

sin (\frac{7 π}{12}) cos (\frac{π}{12})

arccos (\frac{1}{58})

What is the value of tan(pi+arcsin(2/3)) ?
The value of tan(pi+arcsin(2/3)) is (2sqrt(5))/5