What is the value of 2*cos(pi/8)*sin((7pi)/8) ?

The value of 2*cos(pi/8)*sin((7pi)/8) is (sqrt(2))/2

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2cos(pi/8)sin((7pi)/8)

2 \cdot cos (\frac{π}{8}) \cdot sin (\frac{7 π}{8})

\frac{2}{2}

Solution steps

2 cos (\frac{π}{8}) sin (\frac{7 π}{8})

Rewrite using trig identities:

sin (π) + sin (\frac{3 π}{4})

= sin (π) + sin (\frac{3 π}{4})

Use the following trivial identity:

sin (π) = 0

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

= 0 + \frac{2}{2}

Simplify

= \frac{2}{2}

3 (cos (\frac{π}{4}) + i sin (\frac{π}{4}))

arcsin (\frac{6.5}{9.3})

cot (\frac{16 π}{3})

arcsin (sin (\frac{9 π}{4}))

sec (19 5^{\circ})

What is the value of 2*cos(pi/8)*sin((7pi)/8) ?
The value of 2*cos(pi/8)*sin((7pi)/8) is (sqrt(2))/2