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What is the value of tan(45° + x)?

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Question: What is the value of tan(45° + x)?

Options:

  1. tan x
  2. 1 + tan x
  3. (1 - tan x)/(1 + tan x)
  4. 1 - tan x

Correct Answer: 1 + tan x

Solution: 

Using the formula tan(A + B) = (tan A + tan B) / (1 - tan A tan B), we have tan(45° + x) = (1 + tan x) / (1 - 1*tan x) = (1 + tan x).

What is the value of tan(45° + x)?

Practice Questions

Q1
What is the value of tan(45° + x)?
  1. tan x
  2. 1 + tan x
  3. (1 - tan x)/(1 + tan x)
  4. 1 - tan x

Questions & Step-by-Step Solutions

What is the value of tan(45° + x)?
  • Step 1: Identify the angle in the question, which is 45° + x.
  • Step 2: Recall the formula for tangent of a sum of angles: tan(A + B) = (tan A + tan B) / (1 - tan A * tan B).
  • Step 3: In our case, A is 45° and B is x. So we need to find tan(45°) and tan(x).
  • Step 4: We know that tan(45°) = 1.
  • Step 5: Substitute A and B into the formula: tan(45° + x) = (tan(45°) + tan(x)) / (1 - tan(45°) * tan(x)).
  • Step 6: Replace tan(45°) with 1: tan(45° + x) = (1 + tan(x)) / (1 - 1 * tan(x)).
  • Step 7: Simplify the denominator: tan(45° + x) = (1 + tan(x)) / (1 - tan(x)).
  • Step 8: Since 1 - 1 * tan(x) simplifies to 1 - tan(x), we can write: tan(45° + x) = (1 + tan(x)).
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