If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.
Question
If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.
Solution
Sure, here is the step by step solution:
Step 1: We are given that cos A = cos B.
Step 2: We know that the cosine function is positive in the first quadrant, where all acute angles lie.
Step 3: Also, the cosine function is a decreasing function in the first quadrant. This means that if the cosine of two angles is the same, then the angles themselves must be the same.
Step 4: Therefore, if cos A = cos B, then ∠A must be equal to ∠B.
So, we have shown that if ∠A and ∠B are acute angles such that cos A = cos B, then ∠A = ∠B.
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