Math Problem Statement
tan(sin^(-1)x)
Solution
To find , we can proceed with the following steps:
Step-by-step solution:
- Let , so that .
- Now, we need to find . Using the identity for the tangent in terms of sine and cosine:
- Since , we now need to find . Use the Pythagorean identity for sine and cosine: Substituting : Solving for :
- Now, substitute the values of and into the tangent expression:
Thus, .
Final answer:
Do you need further details or have any questions?
Here are 5 related questions for further exploration:
- What is ?
- How would you find ?
- What is the range of values for which is valid?
- How does the identity change for inverse trigonometric functions of complex numbers?
- Can you derive ?
Tip: Always check the domain of the function when dealing with inverse trigonometric functions.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Inverse Trigonometric Functions
Tangent
Pythagorean Identity
Formulas
tan(θ) = sin(θ) / cos(θ)
sin²(θ) + cos²(θ) = 1
tan(sin^(-1)(x)) = x / sqrt(1 - x²)
Theorems
Pythagorean Identity
Tangent Definition in Terms of Sine and Cosine
Suitable Grade Level
Grades 10-12