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

The value of tan(arcsin(4/5)-arccos(1)) is 4/3

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

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

\frac{4}{3}

Decimal Notation

1.33333 \dots

Solution steps

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

Rewrite using trig identities:

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

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

Use the Angle Difference identity:

tan (s - t) = \frac{tan ( s ) - tan ( t )}{1 + tan ( s ) tan ( t )}

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

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

Rewrite using trig identities:

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

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

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{4}{3}

Rewrite using trig identities:

tan (arccos (1)) = 0

tan (arccos (1))

Rewrite using trig identities:

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

Use the following identity:

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

= \frac{1 - 1 ^{2}}{1}

= \frac{1 - 1 ^{2}}{1}

Simplify

= 0

= \frac{\frac{4}{3} - 0}{1 + \frac{4}{3} \cdot 0}

Simplify

= \frac{4}{3}

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

cos (30 0^{\circ}) cos (1 5^{\circ}) - sin (30 0^{\circ}) sin (1 5^{\circ})

2 cos (2 π)

\frac{0.5}{sin ( 0.5 )}

18 sin (7 3^{\circ})

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