What is the value of 2sin(15)cos(75) ?

The value of 2sin(15)cos(75) is 1-(sqrt(3))/2

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2sin(15)cos(75)

2 sin (1 5^{\circ}) cos (7 5^{\circ})

1 - \frac{3}{2}

Decimal Notation

0.13397 \dots

Solution steps

2 sin (1 5^{\circ}) cos (7 5^{\circ})

Rewrite using trig identities:

sin (9 0^{\circ}) - sin (6 0^{\circ})

2 sin (1 5^{\circ}) cos (7 5^{\circ})

Use the Product to Sum identity:

sin (s) cos (t) = \frac{1}{2} (sin (s + t) + sin (s - t))

= 2 \cdot \frac{1}{2} (sin (1 5^{\circ} + 7 5^{\circ}) + sin (1 5^{\circ} - 7 5^{\circ}))

Simplify

= sin (9 0^{\circ}) + sin (- 6 0^{\circ})

Use the following property:

sin (- x) = - sin (x)

sin (- 6 0^{\circ}) = - sin (6 0^{\circ})

= sin (9 0^{\circ}) - sin (6 0^{\circ})

= sin (9 0^{\circ}) - sin (6 0^{\circ})

Use the following trivial identity:

sin (9 0^{\circ}) = 1

sin (9 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}

= 1

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}

= 1 - \frac{3}{2}

cot (arcsin (\frac{5}{13}))

arctan (- \frac{2}{2 3})

cos (\frac{5 π}{4} - \frac{7 π}{6})

- cos (2) (\frac{π}{2})

arcsin (\frac{5}{12 sin ( 3 5 ^{\circ} )})

What is the value of 2sin(15)cos(75) ?
The value of 2sin(15)cos(75) is 1-(sqrt(3))/2