tan ( pi/4 + theda) when tan theda = 1/2
To find the value of tan(pi/4 + θ) when tan(θ) = 1/2, we can use the trigonometric identity for the tangent of the sum of two angles.
The trigonometric identity states that tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)*tan(B))
Let's plug in the values: A = pi/4 and tan(B) = 1/2.
tan(pi/4 + θ) = (tan(pi/4) + tan(θ)) / (1 - tan(pi/4)*tan(θ))
Since tan(pi/4) = 1, we have:
tan(pi/4 + θ) = (1 + tan(θ)) / (1 - tan(θ))
From the given information, we know that tan(θ) = 1/2:
tan(pi/4 + θ) = (1 + 1/2) / (1 - 1/2)
Simplifying further, we get:
tan(pi/4 + θ) = (3/2) / (1/2)
Now, we can simplify the expression by multiplying the numerator and denominator by 2:
tan(pi/4 + θ) = (3/2) * (2/1)
tan(pi/4 + θ) = 3
Therefore, when tan(θ) = 1/2, tan(pi/4 + θ) equals 3.