Final answer:
The exact value of tan(cos⁻¹(7)/(25)) is approximately 5.74.
Step-by-step explanation:
To find the exact value of tan(cos⁻¹(7)/(25)), we can start by finding the value of cos⁻¹(7)/(25). Using the inverse cosine function, we can find the angle whose cosine is 7/25. This angle, let's call it θ, satisfies the equation cos(θ) = 7/25. We can use a calculator to find θ, which is approximately 80.5º.
Next, we can find the tangent of θ by using the tangent function. tan(80.5º) is equal to approximately 5.74.
Therefore, the exact value of tan(cos⁻¹(7)/(25)) is approximately 5.74.