Calculate tan(x-y), if sin x=1/2 and sin y=1/3. 0

We'll write the formula of the tangent of difference of 2
angles.

tan (x-y) = (tan x - tan y)/(1 + tan x*tan
y)

Now, we'll have to establish the signature of tan x a
and tan y. We know from enunciation that, tan x belongs to the first quadrant and it is
has positive and tan y belongs to the second quadrant and it is
negative.

tan x=sin x/cos
x

cos x = sqrt[1 - (sin
x)^2]

cos x = sqrt[1 -
(1/2)^2]

cos x = sqrt(1 -
1/4)

cos x = sqrt3/2

tan x =
(1/2)/(sqrt3/2)

tan x = sqrt
3/3

tan y = -(1/3)/sqrt[1 -
(1/3)^2]

tan y =
-(1/3)/sqrt(8/9)

tan y =
-1/2sqrt2

tan y =
-(sqrt2)/4

tan (x-y) = [(sqrt 3)/3 +
(sqrt2)/4]/[1 - (sqrt6)/12]