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

The value of sin(45)+cos(45)-tan(30) is sqrt(2)-(sqrt(3))/3

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sin(45)+cos(45)-tan(30)

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

2 - \frac{3}{3}

Decimal Notation

0.83686 \dots

Solution steps

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

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 (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:

tan (3 0^{\circ}) = \frac{3}{3}

tan (3 0^{\circ})

tan (x)

periodicity table with

18 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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= \frac{3}{3}

= \frac{2}{2} + \frac{2}{2} - \frac{3}{3}

Simplify

\frac{2}{2} + \frac{2}{2} - \frac{3}{3} : 2 - \frac{3}{3}

\frac{2}{2} + \frac{2}{2} - \frac{3}{3}

Combine the fractions

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

Apply rule

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

= \frac{2 + 2}{2}

Add similar elements:

2 + 2 = 22

= \frac{2 2}{2}

Divide the numbers:

\frac{2}{2} = 1

= 2

= 2 - \frac{3}{3}

= 2 - \frac{3}{3}

arctan (- \frac{2}{- 5})

24.74 cos (117.150 8^{\circ})

sin (cos (π))

(0)^{2} sin (0)

\frac{2 cos ( 2 π )}{3}

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