SOLUTION: If 0° < A, B < 90°, and sinA = cosB, compute cot(A+B)
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Question 1152726: If 0° < A, B < 90°, and sinA = cosB, compute cot(A+B)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
if and only if . We say that angles A and B are complementary
For example, because
Using a calculator, and (both approximate).
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Because we are working with cotangent, let's start with the identity for tangent and rewrite it in terms of cotangent.
Apply reciprocal to both sides.
We will use this later. Call this equation (1).
It might be tempting to use the reciprocal identity but if degrees, then , making to be undefined. Instead it is better to use
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With that in mind, we can compute the cotangent value.
Replace A+B with 90.
Use equation (1).
Use the unit circle to compute cos(90) and sin(90).
Final answer.
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