What is the value of sin(60-45) ?

The value of sin(60-45) is (sqrt(2)(sqrt(3)-1))/4

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sin(60-45)

sin (6 0^{\circ} - 4 5^{\circ})

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

Solution steps

sin (6 0^{\circ} - 4 5^{\circ})

Rewrite using trig identities:

sin (6 0^{\circ}) cos (4 5^{\circ}) - cos (6 0^{\circ}) sin (4 5^{\circ})

= sin (6 0^{\circ}) cos (4 5^{\circ}) - cos (6 0^{\circ}) sin (4 5^{\circ})

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

Use the following trivial identity:

sin (4 5^{\circ}) = \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}

15 \cdot sin (3 0^{\circ})

4 sin (π)

csc (- 13 5^{\circ})

cos (10 5^{\circ}) + cos (1 5^{\circ})

arctan (0.35)

What is the value of sin(60-45) ?
The value of sin(60-45) is (sqrt(2)(sqrt(3)-1))/4