What is the value of sin(165)cos(45) ?

The value of sin(165)cos(45) is (sqrt(3)-1)/4

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sin(165)cos(45)

sin (16 5^{\circ}) cos (4 5^{\circ})

\frac{3 - 1}{4}

Solution steps

sin (16 5^{\circ}) cos (4 5^{\circ})

Rewrite using trig identities:

sin (16 5^{\circ}) = \frac{6 - 2}{4}

Use the following trivial identity:

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

= \frac{6 - 2}{4} \cdot \frac{2}{2}

Simplify

\frac{6 - 2}{4} \cdot \frac{2}{2} : \frac{3 - 1}{4}

= \frac{3 - 1}{4}

arcsin (0.207)

cos (\frac{π}{2}) - i sin (\frac{π}{2})

2 \cdot arctan (1)

\frac{sin ^{3} ( π )}{3}

arcsin (\frac{sin ( 12 0 ^{\circ} )}{2})

What is the value of sin(165)cos(45) ?
The value of sin(165)cos(45) is (sqrt(3)-1)/4