If tan A = cot B, prove that A + B = 90°.
Answer: We have
tan A = cot B ⇒ tan A = tan (90° - B) ⇒ A = 90° - B ⇒ A + B = 90°
tan A = cot B
tan A = tan (90 – B)
A = 90 – B
∴ A + B = 90°.
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