What is the value of sin(pi/4+pi/3) ?

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

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sin(pi/4+pi/3)

sin (\frac{π}{4} + \frac{π}{3})

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

Solution steps

sin (\frac{π}{4} + \frac{π}{3})

Rewrite using trig identities:

sin (\frac{π}{3}) cos (\frac{π}{4}) + cos (\frac{π}{3}) sin (\frac{π}{4})

= sin (\frac{π}{3}) cos (\frac{π}{4}) + cos (\frac{π}{3}) sin (\frac{π}{4})

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

Use the following trivial identity:

sin (\frac{π}{4}) = \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}

arctan (23)

sin (arccos (- \frac{3}{2}))

\frac{tan ( 2 5 ^{\circ} ) + tan ( 11 0 ^{\circ} )}{1 - tan ( 2 5 ^{\circ} ) tan ( 11 0 ^{\circ} )}

- csc^{2} (\frac{π}{6})

cot (- 18 0^{\circ})

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