Statement I: The equation (sin−1x)3+ (cos−1x)3−aπ3=0 has a solution for all a≥132.Statement II: For any x∈R,sin−1x+cos−1x=π2 and 0≤(sin−1x−π4)2≤9π216

Question

Statement I: The equation (sin−1x)3+ (cos−1x)3−aπ3=0 has a solution for all a≥132.Statement II: For any x∈R,sin−1x+cos−1x=π2 and 0≤(sin−1x−π4)2≤9π216
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Solution 1

Statement I: The equation (sin−1x)3+ (cos−1x)3−aπ3=0 has a solution for all a≥132.

Step 1: We know that sin−1x + cos−1x = π/2. This is a standard result in trigonometry.

Step 2: Cubing both sides, we get (sin−1x)3 + (cos−1x)3 + 3sin−1x * cos−1x * (sin−1x + cos−1x) = (π/2)3.

Step 3: Substituting s Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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