In order to calculate the value of cos675°, consider that 675° = 315°.
Moreover, take into account that cos315° = -cos45°, then, you have:
-cos45° = √2/2
for tan(-7π/6), consider that tan(-7π/6) = tan(210°), moreover, cosnider tanx = sinx/cosx, then, you have:
tan(-210°) = sin(-210°)/cos(-210°) = -(1/2)/(√3/2) = -1/√3
