What is the value of 2sin(60)sec(30)cos(45)tan(45) ?

The value of 2sin(60)sec(30)cos(45)tan(45) is square root of 2

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2sin(60)sec(30)cos(45)tan(45)

2 sin (6 0^{\circ}) sec (3 0^{\circ}) cos (4 5^{\circ}) tan (4 5^{\circ})

2

Decimal

1.41421 \dots

Solution steps

2 sin (6 0^{\circ}) sec (3 0^{\circ}) cos (4 5^{\circ}) tan (4 5^{\circ})

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 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{3}{2}

Use the following trivial identity:

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

sec (3 0^{\circ})

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= \frac{2 3}{3}

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 (4 5^{\circ}) = 1

tan (4 5^{\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}

= 1

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

Simplify

2 \cdot \frac{3}{2} \cdot \frac{2 3}{3} \cdot \frac{2}{2} \cdot 1 : 2

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

Multiply fractions:

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

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

Cancel

\frac{3 \cdot 2 3 2 \cdot 2}{2 \cdot 3 \cdot 2} : \frac{3 3 2}{3}

\frac{3 \cdot 2 3 2 \cdot 2}{2 \cdot 3 \cdot 2}

Cancel the common factor:

2

\frac{3 3 2 \cdot 2}{3 \cdot 2}

Cancel the common factor:

2

\frac{3 3 2}{3}

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

\frac{3 3 2}{3} = 2

\frac{3 3 2}{3}

332 = 32

332

Apply radical rule:

a a = a

33 = 3

= 32

= \frac{3 2}{3}

Divide the numbers:

\frac{3}{3} = 1

= 2

= 1 \cdot 2

Multiply:

1 \cdot 2 = 2

= 2

= 2

3 + 2 sin (\frac{π}{4})

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

arctan (\frac{2.5}{1.8})

7 sin (4 0^{\circ})

5 tan (3 0^{\circ})

What is the value of 2sin(60)sec(30)cos(45)tan(45) ?
The value of 2sin(60)sec(30)cos(45)tan(45) is square root of 2