If cos(theta) = -2/sqrt5, and theta is in quadrant II, find the exact value of tan(theta+ pi/4)
+128566 cos (theta) = -2 / √5
sin theta = 1/√5
tan (theta + pi/4) =
sin (theta + pi/4)
_______________ =
cos (theta + pi /4)
sin theta * cos pi/4 + cos theta * sin pi/4
_________________________________ =
costheta * cos pi/4 - sin theta * sin pi/4
{ sin pi/4 = cos pi/4 = 1 /√2 }
1/√2 [ sin theta + cos theta ]
_______________________ =
1 / √2 [ cos theta - sin theta ]
[ 1/√5 + (-2)/√5 ]
_______________ =
[ (-2)/√5 - 1/√5 ]
[ 1 - 2 ] -1 1
________ = ____ = ___
[ -2 - 1 ] -3 3
