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Question

Given: A and  B are less than 90. If A+B = 90, then the value of tan A × tan B is 
  1. \N
  2. 1
  3. not defined
  4. 2


Solution

The correct option is B 1
Given: A+B = 90
B = 90 - A
tan (90θ) = cot θ
tan B = tan (90 - A) = cot A

 tan A × tan B = tan A × cot A

cot A = 1tan A

 tan A × tan B = 1

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