What is the value of (cos(60)+sin(45))cos(30) ?

The value of (cos(60)+sin(45))cos(30) is (sqrt(3)(1+sqrt(2)))/4

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(cos(60)+sin(45))cos(30)

(cos (6 0^{\circ}) + sin (4 5^{\circ})) cos (3 0^{\circ})

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

Decimal Notation

1.04538 \dots

Solution steps

(cos (6 0^{\circ}) + sin (4 5^{\circ})) cos (3 0^{\circ})

Use the following trivial identity:

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

cos (6 0^{\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{1}{2}

Use the following trivial identity:

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

sin (4 5^{\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{2}{2}

Use the following trivial identity:

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

cos (3 0^{\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{3}{2}

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

Simplify

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

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

Combine the fractions

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

Apply rule

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

= \frac{1 + 2}{2}

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

Remove parentheses:

(a) = a

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

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

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

Multiply the numbers:

2 \cdot 2 = 4

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

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

tan (38.6 6^{\circ})

- 1.5 cos (4 0^{\circ})

\frac{( cos ( 2 ( 0.001 ) ) - cos ( 0.001 ) )}{( 0.001 ) ^{2}}

tan (63. 5^{\circ})

sec^{2} (0) - tan^{2} (0)

What is the value of (cos(60)+sin(45))cos(30) ?
The value of (cos(60)+sin(45))cos(30) is (sqrt(3)(1+sqrt(2)))/4