What is the value of sin(arctan(-1)+arcsin(-(sqrt(2))/2)) ?

The value of sin(arctan(-1)+arcsin(-(sqrt(2))/2)) is -1

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

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

- 1

Solution steps

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

Rewrite using trig identities:

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

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

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

Simplify

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

= - 1

tan (\frac{- 159 0 ^{\circ}}{3 cot ^{2} ( 6 0 ^{\circ} )})

cos (46 5^{\circ})

arccos (sin (\frac{5 π}{2}))

4 sin (18 0^{\circ})

sin (\frac{7 π}{8}) - sin (\frac{7 π}{6}) - cot (\frac{π}{3})

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