What is the value of sin(arctan(12/5)+arccos(12/13)) ?

The value of sin(arctan(12/5)+arccos(12/13)) is 1

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sin(arctan(12/5)+arccos(12/13))

sin (arctan (\frac{12}{5}) + arccos (\frac{12}{13}))

1

Solution steps

sin (arctan (\frac{12}{5}) + arccos (\frac{12}{13}))

Rewrite using trig identities:

sin (arctan (\frac{12}{5})) cos (arccos (\frac{12}{13})) + cos (arctan (\frac{12}{5})) sin (arccos (\frac{12}{13}))

= sin (arctan (\frac{12}{5})) cos (arccos (\frac{12}{13})) + cos (arctan (\frac{12}{5})) sin (arccos (\frac{12}{13}))

Rewrite using trig identities:

sin (arctan (\frac{12}{5})) = \frac{12}{13}

Rewrite using trig identities:

cos (arccos (\frac{12}{13})) = \frac{12}{13}

Rewrite using trig identities:

cos (arctan (\frac{12}{5})) = \frac{5}{13}

Rewrite using trig identities:

sin (arccos (\frac{12}{13})) = \frac{5}{13}

= \frac{12}{13} \cdot \frac{12}{13} + \frac{5}{13} \cdot \frac{5}{13}

Simplify

\frac{12}{13} \cdot \frac{12}{13} + \frac{5}{13} \cdot \frac{5}{13} : 1

= 1

arcsin (0.4848)

- \frac{3}{8} cos (2) - \frac{3}{4} sin^{2} (1) + sin^{4} (1) + \frac{3}{8}

20 \cdot sin (3 5^{\circ})

2 sin^{2} (\frac{π}{3})

cos (13 1^{\circ})

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