Question

Write the expression as either the sine, cosine, or tangent of a single angle

Answer 1

We'll use this trig identity
cos(x-y) = cos(x)cos(y) + sin(x)sin(y)
where in this case,
x = pi/3
y = pi/5

So,
cos(x-y) = cos(x)cos(y) + sin(x)sin(y)
cos(pi/3-pi/5) = cos(pi/3)cos(pi/5) + sin(pi/3)sin(pi/5)
cos(pi/3)cos(pi/5) + sin(pi/3)sin(pi/5) = cos(pi/3-pi/5)
cos(pi/3)cos(pi/5) + sin(pi/3)sin(pi/5) = cos(5pi/15-3pi/15)
cos(pi/3)cos(pi/5) + sin(pi/3)sin(pi/5) = cos(2pi/15)

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The answer is cos(2pi/15) which can be written as
`\cos\left((2\pi)/(15)\right)`