use a half- angle identity to find tan(x/2) if sec x = negative 13/2 and pi/2 < x< pi

Answer 1

sin x / (1 + cos x)

sec x = -13/2

cos x = -2/13

Since it is in the 2nd quadrant ( pi/2 < x < pi), the right triangle has vertices (0,0), (-2,0) and (-2, 13)

the missing leg is sqrt ( 165) = sqrt(5 * 33) = sqrt( 5 * 3 * 11)

the sine is sqrt(165)/13

the final answer is sqrt(165)/13 divided by (1 + -2/13) =

sqrt(165)/ 13 divided by (11/13) =

sqrt(165)/13 * 13/ 11 =

sqrt(165)/11