What is the value of sin(arcsin((sqrt(3))/2)+arccos(1)) ?

The value of sin(arcsin((sqrt(3))/2)+arccos(1)) is (sqrt(3))/2

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sin(arcsin((sqrt(3))/2)+arccos(1))

sin (arcsin (\frac{3}{2}) + arccos (1))

\frac{3}{2}

Solution steps

sin (arcsin (\frac{3}{2}) + arccos (1))

Rewrite using trig identities:

sin (arcsin (\frac{3}{2})) cos (arccos (1)) + cos (arcsin (\frac{3}{2})) sin (arccos (1))

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

Rewrite using trig identities:

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

Rewrite using trig identities:

cos (arccos (1)) = 1

Rewrite using trig identities:

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

Rewrite using trig identities:

sin (arccos (1)) = 0

= \frac{3}{2} \cdot 1 + \frac{1}{2} \cdot 0

Simplify

= \frac{3}{2}

sin (11 6^{\circ})

2 cos (2 \cdot 0)

8 cos (12 0^{\circ})

cos (\frac{4 π}{4})

csc (- 3 π)

What is the value of sin(arcsin((sqrt(3))/2)+arccos(1)) ?
The value of sin(arcsin((sqrt(3))/2)+arccos(1)) is (sqrt(3))/2