Question #68f30

1 Answer
t0hierry ยท Stefan V.
Apr 26, 2016

csc((2pi)/3+(5pi)/4) = -(sqrt2 + sqrt6)

Explanation:

That is csc((2pi)/3+(5pi)/4)

sin((2pi)/3+(5pi)/4) = sin((2pi)/3)cos((5pi)/4) + cos((2pi)/3)sin((5pi)/4)

= sqrt3/2 (-sqrt2/2) + (-1/2)(-sqrt2/2)

= (sqrt2 - sqrt6)/4

thus

csc((2pi)/3+(5pi)/4) = 4/(sqrt2 - sqrt6) = -4 * (sqrt2 + sqrt6)/4 = -sqrt2 - sqrt6

Note

23/12 = 2/3 + 5/4

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