Q. 44.7( 16 Votes )

If tan A = cot B

Answer :

Given that, A and B are acute angles.

A < 90° & B < 90°


So, using trigonometric identity, we can say


tan (90° - B) = cot B [, tan (90° - θ) = cot θ]


Replace cot B of RHS by tan (90° - B) in the given question.


tan A = cot B


tan A = tan (90° - B)


Now, comparing the degrees from the above, we get


A = 90° - B


A + B = 90°


Hence, proved that A + B = 90°.


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