If \tan A = \cot B where A and B are acute angles, prove that A + B = 90\degree

Anonymous
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Step 1: Identify the known parts of the problem.
NOTE: \tan A = \cot B
Prove: A + B = 90\degree
Step 2: Make a use of the trigonometric ratios of complimentary angles.
NOTE: We know \cot B = \tan (90\degree - B)............(1)
Step 3: Prove the required equation
EXAMPLE: \tan A = \cot B
\tan A = \tan (90\degree - B) [ \because Equation (1)]
Cancel the \tan on both sides
A = 90\degree - B
A + B = 90\degree
Hence, proved