What is the value of sin(arccos(1/2)+arctan(1)) ?

The value of sin(arccos(1/2)+arctan(1)) is (sqrt(2)(sqrt(3)+1))/4

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sin(arccos(1/2)+arctan(1))

sin (arccos (\frac{1}{2}) + arctan (1))

\frac{2 ( 3 + 1 )}{4}

Solution steps

sin (arccos (\frac{1}{2}) + arctan (1))

Rewrite using trig identities:

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

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

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

Simplify

\frac{3}{2} \cdot \frac{2}{2} + \frac{1}{2} \cdot \frac{2}{2} : \frac{2 ( 3 + 1 )}{4}

= \frac{2 ( 3 + 1 )}{4}

2 \cdot sin (1)

2 \cdot sin (0)

\frac{sin ( 2 ( 0.001 ) )}{2 ( 0.001 )}

cot (\frac{- 2 π}{3})

- tan (\frac{1}{2})

What is the value of sin(arccos(1/2)+arctan(1)) ?
The value of sin(arccos(1/2)+arctan(1)) is (sqrt(2)(sqrt(3)+1))/4