Question

Question #68f30

Answer 1

`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`