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

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

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cos(45)+sin(30)

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

\frac{2 + 1}{2}

Decimal Notation

1.20710 \dots

Solution steps

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

Use the following trivial identity:

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

cos (4 5^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{2}{2}

Use the following trivial identity:

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

sin (3 0^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

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

Simplify

\frac{2}{2} + \frac{1}{2} : \frac{2 + 1}{2}

\frac{2}{2} + \frac{1}{2}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{2 + 1}{2}

= \frac{2 + 1}{2}

arcsin (\frac{4 3}{8})

1 + 4 \cdot sin (\frac{1}{4})

cos (15 0^{\circ}) + i sin (15 0^{\circ})

tan^{2} (3 0^{\circ}) + cos^{2} (6 0^{\circ}) - sec^{2} (3 0^{\circ})

2 cos^{2} (\frac{7 π}{4}) - 1

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