How do you express cos(pi/ 3 ) * sin( ( pi) / 8 ) without using products of trigonometric functions?

1 Answer
Nghi N.
Jul 11, 2016

P = (1/4)sqrt(2 - sqrt2)

Explanation:

P = cos (pi/3).sin (pi/8)
Trig table --> cos (pi/3) = 1/2.
There for, P can be expressed as P = (1/2)sin (pi/8)
We can evaluate sin (pi/8) by using trig identity:
cos 2a = 1 - 2sin^2 a
cos (2pi)/8 = cos (pi/4) = sqrt2/2 = 1 - 2sin^2 (pi/8)
2sin^2 (pi/8) = 1 - sqrt2/2 = (2 - sqrt2)/2
sin^2 (pi/8) = (2 - sqrt2)/4
sin (pi/8) = +- sqrt(2 - sqrt2)/2
Since sin (pi/8) is positive, then,
P = (1/4)sqrt(2 - sqrt2)

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