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

The value of cos(arcsin(4/5)+arccos(3/5)) is -7/25

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

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

- \frac{7}{25}

Solution steps

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

Rewrite using trig identities:

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

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

Rewrite using trig identities:

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

Rewrite using trig identities:

cos (arccos (\frac{3}{5})) = \frac{3}{5}

Rewrite using trig identities:

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

Rewrite using trig identities:

sin (arccos (\frac{3}{5})) = \frac{4}{5}

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

Simplify

\frac{3}{5} \cdot \frac{3}{5} - \frac{4}{5} \cdot \frac{4}{5} : - \frac{7}{25}

= - \frac{7}{25}

90 sin (6 0^{\circ})

cos (2) (90)

3 tan (4 5^{\circ})

tan (0.53)

sec^{6} (0)

What is the value of cos(arcsin(4/5)+arccos(3/5)) ?
The value of cos(arcsin(4/5)+arccos(3/5)) is -7/25