What is the value of sin(arcsin(4/5)+arctan(12/5)) ?

The value of sin(arcsin(4/5)+arctan(12/5)) is 56/65

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sin(arcsin(4/5)+arctan(12/5))

sin (arcsin (\frac{4}{5}) + arctan (\frac{12}{5}))

\frac{56}{65}

Solution steps

sin (arcsin (\frac{4}{5}) + arctan (\frac{12}{5}))

Rewrite using trig identities:

sin (arcsin (\frac{4}{5})) cos (arctan (\frac{12}{5})) + cos (arcsin (\frac{4}{5})) sin (arctan (\frac{12}{5}))

= sin (arcsin (\frac{4}{5})) cos (arctan (\frac{12}{5})) + cos (arcsin (\frac{4}{5})) sin (arctan (\frac{12}{5}))

Rewrite using trig identities:

sin (arcsin (\frac{4}{5})) = \frac{4}{5}

Rewrite using trig identities:

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

= \frac{4}{5} \cdot \frac{5}{13} + \frac{3}{5} \cdot \frac{12}{13}

Simplify

\frac{4}{5} \cdot \frac{5}{13} + \frac{3}{5} \cdot \frac{12}{13} : \frac{56}{65}

= \frac{56}{65}

arccos (\frac{8}{11})

- \frac{2 + 23}{2} \cdot sin (4 4^{\circ}) + 6 \cdot cos (4 4^{\circ})

3 sin (18 0^{\circ}) - 2

180 sin (3 0^{\circ})

9 sin (\frac{π}{2})

What is the value of sin(arcsin(4/5)+arctan(12/5)) ?
The value of sin(arcsin(4/5)+arctan(12/5)) is 56/65