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Popular >

sin(arcsin(1/2)+arctan(-2))

Solution

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

Solution

\frac{5}{10} - \frac{15}{5}

+1

Solution steps

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

Use the following property:

arctan (- x) = - arctan (x)

arctan (- 2) = - arctan (2)

= sin (arcsin (\frac{1}{2}) - arctan (2))

Rewrite using trig identities:

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

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

Rewrite using trig identities:

sin (arcsin (\frac{1}{2})) = \frac{1}{2}

Rewrite using trig identities:

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

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

Simplify

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

= \frac{5}{10} - \frac{15}{5}

Popular Examples

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arcsin (\frac{12}{20})

cos (- \frac{17 π}{3})

cos (\frac{7 π}{5})

Frequently Asked Questions (FAQ)

What is the value of sin(arcsin(1/2)+arctan(-2)) ?
The value of sin(arcsin(1/2)+arctan(-2)) is (sqrt(5)}{10}-\frac{sqrt(15))/5