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

Krishna (last edited 2 years ago) (Expert, Educator @Qalaxia)

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