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

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

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sin(pi/3-pi/4)

sin (\frac{π}{3} - \frac{π}{4})

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

Solution steps

sin (\frac{π}{3} - \frac{π}{4})

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}

arcsin (\frac{12}{20})

cos (- \frac{17 π}{3})

cos (\frac{7 π}{5})

tan (arcsin (\frac{7}{8}))

cos (37. 5^{\circ}) cos (7.5)

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