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

The value of sin(30)tan(45)+tan(30)sin(60) is 1

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sin(30)tan(45)+tan(30)sin(60)

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

1

Solution steps

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

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}

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

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}

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}

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

Simplify

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

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

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

\frac{1}{2} \cdot 1

Multiply:

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

= \frac{1}{2}

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

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

Multiply fractions:

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

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

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

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

Multiply the numbers:

3 \cdot 2 = 6

= \frac{3}{6}

Cancel the common factor:

3

= \frac{1}{2}

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

Apply rule

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

= \frac{1 + 1}{2}

Add the numbers:

1 + 1 = 2

= \frac{2}{2}

Apply rule

\frac{a}{a} = 1

= 1

= 1

cos (arctan (- 3)) + csc (arcsec (2))

sin (\frac{π}{3} - arctan (\frac{1}{3}))

5 + 4 cos (\frac{π}{3})

ln (tan (\frac{π}{4}))

\frac{cos ( \frac{π}{6} )}{( 1 - sin ( \frac{π}{6} ) ) ^{2}}

What is the value of sin(30)tan(45)+tan(30)sin(60) ?
The value of sin(30)tan(45)+tan(30)sin(60) is 1