Answer:
tan 2x=56/33
Step-by-step explanation:
Since x and y lie between 0 and π/4, therefore, their sum (x+y) lies between 0 and π/2. Moreover, since sin(x-y) = 5/13 > 0, therefore, (x-y) also lies between 0 and π/2.
We can now solve the quadratic, (sin(u))[tex]^{2}[/tex] + (cos(u))[tex]^{2}[/tex] = 1 to obtain the value of sin(u) or cos(u), where u = x+y or x-y, since we know that in both cases, u lies in the first quadrant and so, both sin(u) and cos(u) must be positive. Since tan(u) = sin(u)/cos(u), we obtain
tan(x+y) = 3/4
, tan(x-y) = 5/12.
tan(2x) = tan((x+y)+(x-y)) = [tan(x+y) + tan(x-y)]/[1 - (tan(x+y))×(tan(x-y))].
Substituting the values for tan(x+y) and tan(x-y), we get
tan(2x) = 56/33.
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