If 0 ≤ A, B ≤ 90° such that sin A = 1/2 and cos B = 1/2, then A + B =
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We are given that 0° ≤ A, B ≤ 90°, sin A = 1/2, and cos B = 1/2. We need to find the value of A + B.
Step 1: Solve for A using sin A = 1/2
The sine function is defined as:
sin A = opposite/hypotenuse.
From trigonometric values, we know:
sin 30° = 1/2.
Since 0° ≤ A ≤ 90°, the only possible value for A is:
A = 30°.
Step 2: Solve for B using cos B = 1/2
The cosine function is defined as:
cos B = adjacent/hypotenuse.
From trigonometric values, we know:
cos 60° = 1/2.
Since 0° ≤ B ≤ 90°, the only possible value for B is:
B = 60°.
Step 3: Calculate A + B
Now, add the values of A and B:
A + B = 30° + 60° = 90°.
Step 4: Final Answer
The value of A + B is:
c) 90°.
This question related to Chapter 8 Mathematics Class 10th NCERT. From the Chapter 8 Introduction to Trigonometry. Give answer according to your understanding.
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