What is the value of cos(arctan(sqrt(3))+arcsin(1/3)) ?

The value of cos(arctan(sqrt(3))+arcsin(1/3)) is (sqrt(2))/3-(sqrt(3))/6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(arctan(sqrt(3))+arcsin(1/3))

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

\frac{2}{3} - \frac{3}{6}

Solution steps

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

Rewrite using trig identities:

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

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

Rewrite using trig identities:

sin (arctan (3)) = \frac{3}{2}

Rewrite using trig identities:

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

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

Simplify

\frac{1}{2} \cdot \frac{2 2}{3} - \frac{3}{2} \cdot \frac{1}{3} : \frac{2}{3} - \frac{3}{6}

= \frac{2}{3} - \frac{3}{6}

tan (\frac{5 π}{6} - \frac{5 π}{4})

sin (arcsec (8))

- arctan (3)

sin (\frac{π}{4} - \frac{π}{2})

sec (2 6^{\circ})

What is the value of cos(arctan(sqrt(3))+arcsin(1/3)) ?
The value of cos(arctan(sqrt(3))+arcsin(1/3)) is (sqrt(2))/3-(sqrt(3))/6