What is the value of cos(arcsin(4/5)+pi/3) ?

The value of cos(arcsin(4/5)+pi/3) is 3/10-(2sqrt(3))/5

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cos(arcsin(4/5)+pi/3)

cos (arcsin (\frac{4}{5}) + \frac{π}{3})

\frac{3}{10} - \frac{2 3}{5}

Solution steps

cos (arcsin (\frac{4}{5}) + \frac{π}{3})

Rewrite using trig identities:

cos (arcsin (\frac{4}{5})) cos (\frac{π}{3}) - sin (arcsin (\frac{4}{5})) sin (\frac{π}{3})

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

Rewrite using trig identities:

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

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

Rewrite using trig identities:

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

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

= \frac{3}{5} \cdot \frac{1}{2} - \frac{4}{5} \cdot \frac{3}{2}

Simplify

\frac{3}{5} \cdot \frac{1}{2} - \frac{4}{5} \cdot \frac{3}{2} : \frac{3}{10} - \frac{2 3}{5}

= \frac{3}{10} - \frac{2 3}{5}

cos (11 3^{\circ})

25 \cdot sin (6 0^{\circ})

cos (\frac{3 π}{2}) - i sin (\frac{3 π}{2})

sin (0^{2})

15 \cdot tan (2 7^{\circ})

What is the value of cos(arcsin(4/5)+pi/3) ?
The value of cos(arcsin(4/5)+pi/3) is 3/10-(2sqrt(3))/5