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The value of cos(tan^(-1)(x)) is:

Practice Questions

Q1
The value of cos(tan^(-1)(x)) is:
  1. 1/√(1+x^2)
  2. x/√(1+x^2)
  3. √(1+x^2)/x
  4. 0

Questions & Step-by-Step Solutions

The value of cos(tan^(-1)(x)) is:
  • Step 1: Understand that tan^(-1)(x) is the angle whose tangent is x.
  • Step 2: Draw a right triangle where the opposite side is x and the adjacent side is 1. This is because tangent is defined as opposite/adjacent.
  • Step 3: Use the Pythagorean theorem to find the hypotenuse. The hypotenuse is √(1^2 + x^2) = √(1 + x^2).
  • Step 4: Recall that cosine is defined as adjacent/hypotenuse. In our triangle, the adjacent side is 1 and the hypotenuse is √(1 + x^2).
  • Step 5: Write the expression for cosine: cos(tan^(-1)(x)) = adjacent/hypotenuse = 1/√(1 + x^2).
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