The value of (1-tanx) (1-tany) if x + y = 3 / 4

The value of (1-tanx) (1-tany) if x + y = 3 / 4

The answer is 2 Tan (x + y) = - 1, Tan (x + y) = (TaNx + tany) / 1-tanxtany: so TaNx + tany = tanxtany-1, and because the original formula = 1-tanx-tany + tanxtany, the original formula = 1 + 1-tanxtany + tanxtany = 2

If cos (π 4 + x) = 35 and X is the third quadrant angle, then the value of 1 + tanx1 − TaNx is ()
A. −34B. −43C. 34D. 43

∵ cos (π 4 + x) = − 35, ∵ cos π 4cosx sin π 4sinx = - 35, ∵ cosx SiNx = - 325, ∵ 1-2cosxsinx = 1825, ∵ 2sinxcosx = 725, ∵ cosx + SiNx) 2 = 1 + 2sinxcosx = 3225, ∵ x is the third quadrant angle, ∵ cosx + SiNx = - 425 ∵ 1 + tanx1 − TaNx = cosx + sinxcos

Sin (x + y) = 1 / 2, sin (X-Y) = 1 / 3, find the value of TaNx / tany

2sinxcosy=sin(x+y)+sin(x-y)=5/6
2cosxsiny=sin(x+y)-sin(x-y)=1/6
Divide the two expressions to get 5