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Popular >

cos(arctan(-3/4)-arcsin(4/5))

Solution

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

Solution

0

Solution steps

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

Use the following property:

arctan (- x) = - arctan (x)

arctan (- \frac{3}{4}) = - arctan (\frac{3}{4})

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

Use the following property:

cos (- x) = cos (x)

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

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

Rewrite using trig identities:

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

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

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

Simplify

= 0

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Frequently Asked Questions (FAQ)

What is the value of cos(arctan(-3/4)-arcsin(4/5)) ?
The value of cos(arctan(-3/4)-arcsin(4/5)) is 0