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

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

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2sin(75)cos(15)

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

1 + \frac{3}{2}

Decimal Notation

1.86602 \dots

Solution steps

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

Rewrite using trig identities:

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

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

Simplify

= 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}

25 cos (3 7^{\circ})

100 \cdot sin (2 0^{\circ})

arctan (\frac{2.6}{- 1.1})

sin (\frac{1}{\frac{2}{9 π}})

- 1160 sin (4 6^{\circ}) + 570 sin (2 2^{\circ})

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