If sin^(-1)(x) + cos^(-1)(x) = π/2, then the value of x is:
Practice Questions
1 question
Q1
If sin^(-1)(x) + cos^(-1)(x) = π/2, then the value of x is:
0
1
-1
1/2
The equation sin^(-1)(x) + cos^(-1)(x) = π/2 holds for all x in the domain of the functions, which is [-1, 1]. Therefore, x can be any value in this range.
Questions & Step-by-step Solutions
1 item
Q
Q: If sin^(-1)(x) + cos^(-1)(x) = π/2, then the value of x is:
Solution: The equation sin^(-1)(x) + cos^(-1)(x) = π/2 holds for all x in the domain of the functions, which is [-1, 1]. Therefore, x can be any value in this range.
Steps: 4
Step 1: Understand the functions involved. sin^(-1)(x) is the inverse sine function, and cos^(-1)(x) is the inverse cosine function.
Step 2: Recall the property of these functions. The equation sin^(-1)(x) + cos^(-1)(x) = π/2 is a known identity in trigonometry.
Step 3: Recognize the domain of the functions. The values of x for which these functions are defined are between -1 and 1, inclusive.
Step 4: Conclude that since the equation holds true for all x in the domain, x can be any value from -1 to 1.
