What is the value of tan(arcsin(5/13)+arccos(1)) ?

The value of tan(arcsin(5/13)+arccos(1)) is 5/12

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tan(arcsin(5/13)+arccos(1))

tan (arcsin (\frac{5}{13}) + arccos (1))

\frac{5}{12}

Decimal Notation

0.41666 \dots

Solution steps

tan (arcsin (\frac{5}{13}) + arccos (1))

Rewrite using trig identities:

\frac{tan ( arcsin ( \frac{5}{13} ) ) + tan ( arccos ( 1 ) )}{1 - tan ( arcsin ( \frac{5}{13} ) ) tan ( arccos ( 1 ) )}

tan (arcsin (\frac{5}{13}) + arccos (1))

Use the Angle Sum identity:

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

= \frac{tan ( arcsin ( \frac{5}{13} ) ) + tan ( arccos ( 1 ) )}{1 - tan ( arcsin ( \frac{5}{13} ) ) tan ( arccos ( 1 ) )}

= \frac{tan ( arcsin ( \frac{5}{13} ) ) + tan ( arccos ( 1 ) )}{1 - tan ( arcsin ( \frac{5}{13} ) ) tan ( arccos ( 1 ) )}

Rewrite using trig identities:

tan (arcsin (\frac{5}{13})) = \frac{5}{12}

tan (arcsin (\frac{5}{13}))

Rewrite using trig identities:

tan (arcsin (\frac{5}{13})) = \frac{( \frac{5}{13} ) 1 - ( \frac{5}{13} ) ^{2}}{1 - ( \frac{5}{13} ) ^{2}}

Use the following identity:

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

= \frac{( \frac{5}{13} ) 1 - ( \frac{5}{13} ) ^{2}}{1 - ( \frac{5}{13} ) ^{2}}

= \frac{\frac{5}{13} 1 - ( \frac{5}{13} ) ^{2}}{1 - ( \frac{5}{13} ) ^{2}}

Simplify

= \frac{5}{12}

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{5}{12} + 0}{1 - \frac{5}{12} \cdot 0}

Simplify

= \frac{5}{12}

sec (48 0^{\circ})

arctan (\frac{16}{3})

sin (2 π^{2})

2 tan (1)

arccos (\frac{3}{6})

What is the value of tan(arcsin(5/13)+arccos(1)) ?
The value of tan(arcsin(5/13)+arccos(1)) is 5/12