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Evaluate sin(tan^(-1)(x)).
Evaluate sin(tan^(-1)(x)).
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Practice Questions
1 question
Q1
Evaluate sin(tan^(-1)(x)).
x/√(1+x^2)
√(1-x^2)
1/x
x
Show Solution
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Using the identity, sin(tan^(-1)(x)) = x/√(1+x^2).
Questions & Step-by-step Solutions
1 item
Q
Q: Evaluate sin(tan^(-1)(x)).
Solution:
Using the identity, sin(tan^(-1)(x)) = x/√(1+x^2).
Steps: 6
Show Steps
Step 1: Understand that tan^(-1)(x) is the angle whose tangent is x.
Step 2: Let θ = tan^(-1)(x). This means tan(θ) = x.
Step 3: Recall the definition of tangent: tan(θ) = opposite/adjacent. Here, we can think of opposite = x and adjacent = 1.
Step 4: Use the Pythagorean theorem to find the hypotenuse: hypotenuse = √(opposite^2 + adjacent^2) = √(x^2 + 1).
Step 5: Now, we can find sin(θ). Since sin(θ) = opposite/hypotenuse, we have sin(θ) = x/√(x^2 + 1).
Step 6: Therefore, sin(tan^(-1)(x)) = x/√(1 + x^2).
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