Question: If sin^(-1)(x) + cos^(-1)(x) = π/2, then what is the value of x?
Options:
0
1
-1
1/2
Correct Answer: 0
Solution:
Using the identity sin^(-1)(x) + cos^(-1)(x) = π/2, we can conclude that x can take any value in the range [-1, 1].
If sin^(-1)(x) + cos^(-1)(x) = π/2, then what is the value of x?
Practice Questions
Q1
If sin^(-1)(x) + cos^(-1)(x) = π/2, then what is the value of x?
0
1
-1
1/2
Questions & Step-by-Step Solutions
If sin^(-1)(x) + cos^(-1)(x) = π/2, then what is the value of x?
Correct Answer: x can be any value in the range [-1, 1]
Step 1: Understand the notation sin^(-1)(x) and cos^(-1)(x). These represent the inverse sine and inverse cosine functions, respectively.
Step 2: Recall the identity that states sin^(-1)(x) + cos^(-1)(x) = π/2 for any value of x in the range [-1, 1].
Step 3: Since the equation given in the question is exactly this identity, it holds true for all x in the range [-1, 1].
Step 4: Therefore, the value of x can be any number between -1 and 1, inclusive.
Inverse Trigonometric Functions – Understanding the relationship between the inverse sine and cosine functions, specifically the identity that states sin^(-1)(x) + cos^(-1)(x) = π/2.
Domain and Range of Functions – Recognizing that the values of x for which the inverse trigonometric functions are defined are limited to the interval [-1, 1].
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