What is the value of sin(45)cos(30)+sin(30)cos(45) ?

The value of sin(45)cos(30)+sin(30)cos(45) is (sqrt(6)+sqrt(2))/4

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sin(45)cos(30)+sin(30)cos(45)

sin (4 5^{\circ}) cos (3 0^{\circ}) + sin (3 0^{\circ}) cos (4 5^{\circ})

\frac{6 + 2}{4}

Solution steps

sin (4 5^{\circ}) cos (3 0^{\circ}) + sin (3 0^{\circ}) cos (4 5^{\circ})

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

Use the following trivial identity:

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

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

Simplify

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

= \frac{6 + 2}{4}

\frac{1}{cos ( 2 5 ^{\circ} )}

\frac{5}{2} sin (\frac{4 π}{3} - π)

π sec (π)

40 \cdot cos (5 3^{\circ})

arcsin (- \frac{π}{3})

What is the value of sin(45)cos(30)+sin(30)cos(45) ?
The value of sin(45)cos(30)+sin(30)cos(45) is (sqrt(6)+sqrt(2))/4