What is the value of cos(arcsin(1/3)-arctan(1/2)) ?

The value of cos(arcsin(1/3)-arctan(1/2)) is (4sqrt(10)+sqrt(5))/(15)

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cos(arcsin(1/3)-arctan(1/2))

cos (arcsin (\frac{1}{3}) - arctan (\frac{1}{2}))

\frac{4 10 + 5}{15}

Solution steps

cos (arcsin (\frac{1}{3}) - arctan (\frac{1}{2}))

Rewrite using trig identities:

cos (arcsin (\frac{1}{3})) cos (arctan (\frac{1}{2})) + sin (arcsin (\frac{1}{3})) sin (arctan (\frac{1}{2}))

= cos (arcsin (\frac{1}{3})) cos (arctan (\frac{1}{2})) + sin (arcsin (\frac{1}{3})) sin (arctan (\frac{1}{2}))

Rewrite using trig identities:

cos (arcsin (\frac{1}{3})) = \frac{2 2}{3}

Rewrite using trig identities:

cos (arctan (\frac{1}{2})) = \frac{2 5}{5}

Rewrite using trig identities:

sin (arcsin (\frac{1}{3})) = \frac{1}{3}

Rewrite using trig identities:

sin (arctan (\frac{1}{2})) = \frac{5}{5}

= \frac{2 2}{3} \cdot \frac{2 5}{5} + \frac{1}{3} \cdot \frac{5}{5}

Simplify

\frac{2 2}{3} \cdot \frac{2 5}{5} + \frac{1}{3} \cdot \frac{5}{5} : \frac{4 10 + 5}{15}

= \frac{4 10 + 5}{15}

1 - sin (\frac{3 π}{2})

ln (cos (\frac{π}{3}))

\frac{sin ( 4 )}{2}

1 + cos (\frac{π}{2})

cos (- 48 0^{\circ})

What is the value of cos(arcsin(1/3)-arctan(1/2)) ?
The value of cos(arcsin(1/3)-arctan(1/2)) is (4sqrt(10)+sqrt(5))/(15)