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Find the value of cos(tan^(-1)(1)).

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Question: Find the value of cos(tan^(-1)(1)).

Options:

  1. 1/√2
  2. 1/2
  3. √2/2
  4. √3/2

Correct Answer: √2/2

Solution: 

cos(tan^(-1)(1)) = 1/√2

Find the value of cos(tan^(-1)(1)).

Practice Questions

Q1
Find the value of cos(tan^(-1)(1)).
  1. 1/√2
  2. 1/2
  3. √2/2
  4. √3/2

Questions & Step-by-Step Solutions

Find the value of cos(tan^(-1)(1)).
  • Step 1: Understand that tan^(-1)(1) means we are looking for an angle whose tangent is 1.
  • Step 2: Recall that the tangent of 45 degrees (or Ο€/4 radians) is 1.
  • Step 3: Therefore, tan^(-1)(1) = 45 degrees (or Ο€/4 radians).
  • Step 4: Now, we need to find the cosine of this angle: cos(45 degrees).
  • Step 5: The cosine of 45 degrees is known to be 1/√2.
  • Step 6: Thus, we conclude that cos(tan^(-1)(1)) = 1/√2.
  • Inverse Trigonometric Functions – Understanding how to evaluate the cosine of an angle derived from the inverse tangent function.
  • Right Triangle Relationships – Using the properties of right triangles to find the cosine value based on the tangent value.
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