What is the value of 4sin(pi/8)cos(pi/8) ?

The value of 4sin(pi/8)cos(pi/8) is square root of 2

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4sin(pi/8)cos(pi/8)

4 sin (\frac{π}{8}) cos (\frac{π}{8})

2

Solution steps

4 sin (\frac{π}{8}) cos (\frac{π}{8})

Rewrite using trig identities:

sin (\frac{π}{8}) cos (\frac{π}{8}) = \frac{sin ( \frac{π}{4} )}{2}

= 4 \cdot \frac{sin ( \frac{π}{4} )}{2}

4 \cdot \frac{sin ( \frac{π}{4} )}{2} = 2 sin (\frac{π}{4})

= 2 sin (\frac{π}{4})

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

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

Simplify

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

= 2

sin (26 5^{\circ})

7 sin (6 0^{\circ})

arctan (\frac{8}{- 6})

6 cos (\frac{π}{6}) cos (\frac{π}{3})

cos (π (1))

What is the value of 4sin(pi/8)cos(pi/8) ?
The value of 4sin(pi/8)cos(pi/8) is square root of 2