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2cos−1x = cos−1(2x2−1)holds true for all
  • a)
    |x| ≤ 1/2
  • b)
    |x|⩽1
  • c)
    0⩽x⩽1
  • d)
    none of these.
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
2cos−1x = cos−1(2x2−1)holds true for alla)|x|≤1/2...
This is true for all real values of x ∈ [0,1].
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Most Upvoted Answer
2cos−1x = cos−1(2x2−1)holds true for alla)|x|≤1/2...
Given Equation:
2cos-1x = cos-1(2x2 - 1)

Explanation:
To understand the given equation, let's break it down step by step:

Step 1: Rewrite the equation using the definition of inverse trigonometric functions.
2cos-1x = cos-1(2x2 - 1)
cos(2cos-1x) = 2x2 - 1

Step 2: Use the double angle formula for cosine:
cos(2θ) = 2cos2θ - 1

Step 3: Substitute 2cos-1x as θ in the double angle formula:
2cos2(cos-1x) - 1 = 2x2 - 1
2x2 - 1 = 2x2 - 1

Step 4: Simplify the equation:
2x2 - 1 = 2x2 - 1

Conclusion:
The given equation 2cos-1x = cos-1(2x2 - 1) holds true for all values of x where 0 ≤ x ≤ 1. Therefore, the correct answer is option 'C' (0 ≤ x ≤ 1).
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Question Description
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