x and y represent two angles in standard position. x has its terminal arm in the first quadrant and y has its terminal arm in the third quadrant. If cosx=5/13 and cosy = -5/13 then find the value of

2sinx+2siny+2cosx-2tanx+tany+2cosy

1 answer

if cosx = 5/13, (recognize the 5,12,13 triangle ?)
sinx = 12/13
tanx = 12/5

if cosy = -5/13 and y is in III
siny = -12/13
tany = 12/5

2sinx+2siny+2cosx-2tanx+tany+2cosy
= 2(12/13) + 2(-12/13) + 2(5/13) -2(12/5) + (12/5) + 2(-5/13)
= - 12/5 or -2.4