What is the value of cos(arcsin(3/5)+arctan(5/12)) ?

The value of cos(arcsin(3/5)+arctan(5/12)) is 33/65

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(arcsin(3/5)+arctan(5/12))

cos (arcsin (\frac{3}{5}) + arctan (\frac{5}{12}))

\frac{33}{65}

Solution steps

cos (arcsin (\frac{3}{5}) + arctan (\frac{5}{12}))

Rewrite using trig identities:

cos (arctan (\frac{5}{12})) cos (arcsin (\frac{3}{5})) - sin (arctan (\frac{5}{12})) sin (arcsin (\frac{3}{5}))

= cos (arctan (\frac{5}{12})) cos (arcsin (\frac{3}{5})) - sin (arctan (\frac{5}{12})) sin (arcsin (\frac{3}{5}))

Rewrite using trig identities:

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

Rewrite using trig identities:

sin (arcsin (\frac{3}{5})) = \frac{3}{5}

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

Simplify

\frac{12}{13} \cdot \frac{4}{5} - \frac{5}{13} \cdot \frac{3}{5} : \frac{33}{65}

= \frac{33}{65}

arcsin (- 0.9)

arcsin (- 0.6)

cos (- 0.6)

arctan (- 44)

arctan (- 11)

What is the value of cos(arcsin(3/5)+arctan(5/12)) ?
The value of cos(arcsin(3/5)+arctan(5/12)) is 33/65