Question #68f30

1 Answer
Apr 26, 2016

csc((2pi)/3+(5pi)/4) = -(sqrt2 + sqrt6)csc(2π3+5π4)=(2+6)

Explanation:

That is csc((2pi)/3+(5pi)/4)csc(2π3+5π4)

sin((2pi)/3+(5pi)/4) = sin((2pi)/3)cos((5pi)/4) + cos((2pi)/3)sin((5pi)/4)sin(2π3+5π4)=sin(2π3)cos(5π4)+cos(2π3)sin(5π4)

= sqrt3/2 (-sqrt2/2) + (-1/2)(-sqrt2/2)=32(22)+(12)(22)

= (sqrt2 - sqrt6)/4=264

thus

csc((2pi)/3+(5pi)/4) = 4/(sqrt2 - sqrt6) = -4 * (sqrt2 + sqrt6)/4 = -sqrt2 - sqrt6csc(2π3+5π4)=426=42+64=26

Note

23/12 = 2/3 + 5/42312=23+54