SOLUTION: If sinA = cosB, compute csc(A+B).

Question 1193330: If sinA = cosB, compute csc(A+B).
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Answer: 1

Reason:

If A+B = 90, then cos(A) = sin(B), and vice versa.
We can also say sin(A) = cos(B) when A+B = 90.
This can be visually proven by drawing out a right triangle with acute angles A and B. I'll leave this proof for the student to carry out.

Therefore,
csc(A+B) = 1/sin(A+B) = 1/sin(90) = 1/1 = 1

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