If tan(x+y)=2 and tanx=1.find tan^-1?
tan(x+y) = (tanx + tany)/(1 - tanxtany)
2 = (1 + tany)/(1 - tany)
1 + tany = 2 - 2tany
3tany = 1
tany = 1/3
Don't know what inverse you want when you ask for tan^-1
if tanx = 1
x = π/4
if tany = 1/3
y = .32175..
if tan(x+y) = 2
x + y = 1.107148..
verified in π/4 + .32175 = 1.107..
To find the value of tan^-1, we need to find the angle whose tangent is equal to the given value.
Given information:
tan(x+y) = 2
tanx = 1
Using the identities of trigonometric functions, we can rewrite tan(x+y) as follows:
tan(x+y) = (tanx + tany) / (1 - tanx*tany)
Substituting the given values:
2 = (1 + tany) / (1 - 1*tany)
Now we can solve this equation to find the value of tany.
Multiplying both sides of the equation by (1 - tany):
2(1 - tany) = 1 + tany
Expanding the left side:
2 - 2tany = 1 + tany
Combining like terms:
3tany = 2 -1
3tany = 1
Dividing both sides by 3:
tany = 1/3
So, the value of tany is 1/3.
Now we can use the inverse tangent function (tan^-1) to find the angle whose tangent is 1/3:
tan^-1(1/3)
Using a calculator or a table of values, the approximate value of tan^-1(1/3) is approximately 18.43 degrees.
Therefore, the value of tan^-1(1) is approximately 18.43 degrees.