The value of sin(1/2.arccot(-3/4)) + cos (1/2.arccot(-3/4)) is equal to:
A)1
B)(3√20)/10
C)√2.sin ((3π/4) + 1/2.arccot 3/4)
D)√2.sin(π -1/2.arccot 4/3)
More than one options may be correct.
How far have you gotten?
1) Remember that arccot(x) produces an ANGLE, usually on $\displaystyle (0,\pi)$.
2) Do you have half-angle formulas? You will need them.
3) There are some right triangles in your future.
4) Don't forget what Quadrant you are in. (Actually, you tell me if this matters. Maybe symmetry will bail you out.)