Answer:

2tan^-¹ x = tan^-¹ (2x/1-x²)

Step-by-step explanation:

tan( 2tan^-¹ 1/5- tan^-¹ 1)

x = 1/5

on solving:

tan(tan^-¹ 5/12- tan^-¹ 1). tan-^¹ x- tan^-¹ y = tan^-¹ (x+y/1+xy)

tan(tan^-¹((-7/12)/(17/12))

tan(tan^-¹ (-7/17))

-7/17 is the answer

Verified answer

[tex]\huge{\boxed{\mathfrak{Answer}}}[/tex]

2 tan-1(1/5) = tan-1(1/5) + tan-1(1/5)

Using the formula tan-1(x) + tan-1(y) = tan-1[(x + y)/ (1 – xy)],

• = tan-1[{(1/5) + (1/5)}/ {1 – (1/5)(1/5)}]

• = tan-1[(2/5)/ {(25 – 1)/25}]

• = tan-1[(2/5)/ (24/25)]

• = tan-1(5/12)

Now,

• tan[2 tan-1(1/5) – (π/4)] = tan[tan-1(5/12) – (π/4)]

Using the formula tan(A – B) = (tan A – tan B)/(1 + tan A tan B),

• = [tan{tan-1(5/12)} – tan π/4]/ [1 + tan{tan-1(5/12)} tan π/4]

• = [(5/12) – 1]/ [1 + (5/12)(1)]

• = (5 – 12)/(12 + 5)

• = -7/17

Hope it helps uh! :)