If sin^(-1)(x) + cos^(-1)(x) = π/2, then the value of x is:

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Question: If sin^(-1)(x) + cos^(-1)(x) = π/2, then the value of x is:

Options:

0
1
-1
1/2

Correct Answer: 0

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.

If sin^(-1)(x) + cos^(-1)(x) = π/2, then the value of x is:

Practice Questions

If sin^(-1)(x) + cos^(-1)(x) = π/2, then the value of x is:

0
1
-1
1/2

Questions & Step-by-Step Solutions

If sin^(-1)(x) + cos^(-1)(x) = π/2, then the value of x is:

Correct Answer: Any value in the range [-1, 1]

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.

Inverse Trigonometric Functions – The relationship between the inverse sine and inverse cosine functions, specifically that their sum equals π/2 for any x in the domain [-1, 1].
Domain of Functions – Understanding the valid input range for the inverse sine and cosine functions, which is limited to the interval [-1, 1].

If sin^(-1)(x) + cos^(-1)(x) = π/2, then the value of x is:

What’s inside this PDF?

If sin^(-1)(x) + cos^(-1)(x) = π/2, then the value of x is:

Practice Questions

Questions & Step-by-Step Solutions

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