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

The value of sin(30)cos(45)+cos(30)sin(45) is (sqrt(2)(1+sqrt(3)))/4

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

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

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

Solution steps

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

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

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

Use the following trivial identity:

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

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

Simplify

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

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

cos (13 4^{\circ})

- cos (0) - sin (0)

cos (arcsin (\frac{3}{5}) - arctan (\frac{5}{12}))

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

58 sin (5 4^{\circ})

What is the value of sin(30)cos(45)+cos(30)sin(45) ?
The value of sin(30)cos(45)+cos(30)sin(45) is (sqrt(2)(1+sqrt(3)))/4